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BEGIN:VEVENT
SUMMARY:Arnulf Jentzen (University of Münster)
DTSTART:20200824T130000Z
DTEND:20200824T140000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/1
DESCRIPTION:by Arnulf Jentzen (University of Münster) as part of "Partial
Differential Equations and Applications" Webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julio D. Rossi (Universidad de Buenos Aires)
DTSTART:20200831T130000Z
DTEND:20200831T140000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/2
DESCRIPTION:Title: A game theoretical approach for a nonlinear system driven by ellipti
c operators\nby Julio D. Rossi (Universidad de Buenos Aires) as part o
f "Partial Differential Equations and Applications" Webinar\n\n\nAbstract\
nThis talk is based on the interplay between partial differential equation
s and probability. \n\nWe find approximations using game theory to viscosi
ty solutions to an elliptic system governed by two different operators (th
e Laplacian and the infinity Laplacian). \n\nWe analyze a game that combin
es Tug-of-War with Random Walks in two different boards with a positive pr
obability of jumping from one board to the other and we prove that the val
ue functions for this game converge uniformly to a viscosity solution of a
n elliptic system as the step size goes to zero.\n\nIn addition\, we show
uniqueness for the elliptic system using pure PDE techniques.\n\nJoint wor
k with A. Miranda (Buenos Aires).\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Bartsch (Universität Gießen)
DTSTART:20200907T130000Z
DTEND:20200907T140000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/3
DESCRIPTION:Title: Normalized solutions of nonlinear elliptic problems\nby Thomas B
artsch (Universität Gießen) as part of "Partial Differential Equations a
nd Applications" Webinar\n\n\nAbstract\nThe talk will be concerned with th
e existence of $L^2$ normalized solutions to nonlinear elliptic equations
and systems. A model problem is the system of nonlinear Schrödinger equat
ions\n\n$$-\\Delta u+\\lambda_1 u = \\mu_1 u^3 + \\beta u v^2 \\qquad \\in
\\mathbb{R}^3$$\n$$-\\Delta v+\\lambda_2 v = \\mu_2 v^3 + \\beta u^2 v \\
qquad \\in \\mathbb{R}^3$$\n\nwith normalization constraints\n\n$$\\int_{\
\mathbb{R}^3} u^2 = a^2 \\quad \\text{and}\\quad \\int_{\\mathbb{R}^3} v^
2 = b^2 \\\, .$$\n\nWhereas nonlinear elliptic equations and systems have
been investigated intensively since the 1960s\, in comparison surprisingly
little\nis known about solutions with prescribed $L^2$ norms. We discuss
this\nproblem and survey recent results.\nThe talk is based on joint work
with Louis Jeanjean\, Yanyan Liu\,\nZhaoli Liu\, Nicola Soave\, Xuexiu Zho
ng\, Wenming Zou.\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weinan E (Princeton University)
DTSTART:20200914T130000Z
DTEND:20200914T140000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/4
DESCRIPTION:Title: PDE problems that arise from machine learning\nby Weinan E (Prin
ceton University) as part of "Partial Differential Equations and Applicati
ons" Webinar\n\n\nAbstract\nTwo kinds of PDE problems arise from machine l
earning. The continuous formulation of machine learning naturally gives ri
se to some very elegant and challenging PDE (more precisely partial differ
ential and integral equations) problems. It is likely that understanding
these PDE problems will become fundamental issues in the mathematical theo
ry of machine learning.\nMachine learning-based algorithms for PDEs also l
ead to new questions about these PDEs\, for example\, new kinds of a prior
i estimates that are suited for the machine learning model. I will discuss
both kinds of problems.\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudio Muñoz (Universidad de Chile)
DTSTART:20200921T130000Z
DTEND:20200921T140000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/5
DESCRIPTION:Title: Understanding soliton dynamics in Boussinesq models\nby Claudio
Muñoz (Universidad de Chile) as part of "Partial Differential Equations a
nd Applications" Webinar\n\n\nAbstract\nThe purpose of this talk is to des
cribe in simple terms the soliton problem for several Boussinesq models\,
including good\, improved and abcd systems. The problem is not simple\, be
cause some particular unstable behavior present in each system above menti
oned. The idea is to explain the particularities of each system\, previous
and recent results\, and future research\, in simple words.\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yihong Du (University of New England)
DTSTART:20200928T130000Z
DTEND:20200928T140000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/6
DESCRIPTION:Title: Long-time dynamics of the Fisher-KPP equation with nonlocal diffusio
n and free boundary\nby Yihong Du (University of New England) as part
of "Partial Differential Equations and Applications" Webinar\n\n\nAbstract
\nWe consider the Fisher-KPP equation with free boundary and "nonlocal dif
fusion". We show the problem is well-posed\, and its long-time dynamical b
ehavior is governed by a spreading-vanishing dichotomy. Moreover\, we comp
letely determine the spreading profile\, which may have a finite spreading
speed determined by a semi-wave problem\, or have infinite spreading spee
d (accelerated spreading)\, according to whether a threshold condition on
the kernel function is satisfied. Further more\, for some typical kernel f
unctions\, we obtain sharp estimates of the spreading speed (whether finit
e or infinite).\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Em Karniadakis (Brown University and MIT)
DTSTART:20201005T130000Z
DTEND:20201005T140000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/7
DESCRIPTION:Title: From PINNs to DeepOnets: Approximating functions\, functionals\, and
operators using deep neural networks\nby George Em Karniadakis (Brown
University and MIT) as part of "Partial Differential Equations and Applic
ations" Webinar\n\n\nAbstract\nWe will present a new approach to develop a
data-driven\, learning-based framework for predicting outcomes of physica
l and biological systems\, governed by PDEs\, and for discovering hidden p
hysics from noisy data. We will introduce a deep learning approach based o
n neural networks (NNs) and generative adversarial networks (GANs). We als
o introduce new NNs that learn functionals and nonlinear operators from fu
nctions and corresponding responses for system identification. Unlike othe
r approaches that rely on big data\, here we “learn” from small data b
y exploiting the information provided by the physical conservation laws\,
which are used to obtain informative priors or regularize the neural netwo
rks. We will also make connections between Gauss Process Regression and NN
s and discuss the new powerful concept of meta-learning. We will demonstra
te the power of PINNs for several inverse problems in fluid mechanics\, so
lid mechanics and biomedicine including wake flows\, shock tube problems\,
material characterization\, brain aneurysms\, etc\, where traditional met
hods fail due to lack of boundary and initial conditions or material prope
rties.\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shi Jin (Shanghai Jiao Tong University)
DTSTART:20201012T130000Z
DTEND:20201012T140000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/8
DESCRIPTION:Title: Random Batch Methods for classical and quantum N-body problems\n
by Shi Jin (Shanghai Jiao Tong University) as part of "Partial Differentia
l Equations and Applications" Webinar\n\n\nAbstract\nWe first develop rand
om batch methods for classical interacting particle systems with large nu
mber of particles. These methods use small but random batches for particle
interactions\, thus the computational cost is reduced from O(N^2) per tim
e step to O(N)\, for a system with N particles with binary interactions. F
or one of the methods\, we give a particle number independent error estima
te under some special interactions.\n\nThis method is also extended to qua
ntum Monte-Carlo methods for N-body Schrodinger equation and will be shown
to have significant gains in computational speed up over the classical M
etropolis-Hastings algorithm and the Langevin dynamics based Euler-Maruyam
a method for statistical samplings of general distributions for interactin
g particles. \n\nFor quantum N-body Schrodinger equation\, we also obtain
\, for pair-wise random interactions\, a convergence estimate for the Wign
er transform of the single-particle reduced density matrix of the particle
system at time t that is uniform in N > 1 and independent of the Planck c
onstant \\hbar. To this goal we need to introduce a new metric specially t
ailored to handle at the same time the difficulties pertaining to the smal
l \\hbar regime (classical limit)\, and those pertaining to the large N re
gime (mean-field limit).\n\nThis talk is based on joint works with Lei Li\
, Jian-Guo Liu\, Francois Golse\, Thierry Paul and Xiantao Li.\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshikazu Giga (University of Tokyo)
DTSTART:20201019T130000Z
DTEND:20201019T140000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/9
DESCRIPTION:Title: On total variation flow type equations\nby Yoshikazu Giga (Unive
rsity of Tokyo) as part of "Partial Differential Equations and Application
s" Webinar\n\n\nAbstract\nThe classical total variation flow is the $L^2$
gradient flow of the total variation. The total variation of a function u
is one-Dirichlet energy\, i.e.\,$ \\int |Du| dx$. Different from the Diric
hlet energy $\\int |Du|^2 dx/2$\, the energy density is singular at the pl
ace where the slope of the function u equals zero. Because of this structu
re\, its gradient flow is actually non-local in the sense that the speed o
f slope zero part (called a facet) is not determined by infinitesimal quan
tity. Thus\, the definition of a solution itself is a nontrivial issue eve
n for the classical total variation flow. This becomes more serious if the
re is non-uniform driving force term.\n\nRecently\, there need to study va
rious types of such equations. A list of examples includes the total varia
tion map flow as well as the classical total variation flow and its fourth
order version in image de-noising\, crystalline mean curvature flow or fo
urth order total variation flow in crystal growth problems which are impor
tant models in materials science below roughening temperature.\n\nIn this
talk\, we survey recent progress on these equations with special emphasis
on a crystalline mean curvature flow whose solvability was left open more
than ten years. We shall give a global-in-time unique solvability in the l
evel-set sense. It includes a recent extension when there is spatially non
-uniform driving force term which is going to be published in the journal
SN Partial Differential Equations. These last well-posedness results are
based on my joint work with N. Požár (Kanazawa University) whose basic i
dea depends on my earlier joint work with M.-H. Giga (The University of To
kyo) and N. Požár.\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaeyoung Byeon (KAIST)
DTSTART:20201109T140000Z
DTEND:20201109T150000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/10
DESCRIPTION:Title: Nonlinear Schrödinger systems with large interaction forces betwee
n different components\nby Jaeyoung Byeon (KAIST) as part of "Partial
Differential Equations and Applications" Webinar\n\n\nAbstract\nThere have
been many studies on the asymptotic behavior of low energy solutions for
a single elliptic equation as an involved parameter approaches to a thresh
old. In this case\, the asymptotic behavior depends on a balance between t
he differential operator and nonlinearity\, and their interaction with a g
eometry of a underlying domain. On the other hand\, even though the ellipt
ic systems coming from nonlinear Schrödinger systems have a simple lookin
g interaction terms\, even the construction of nontrivial low energy solut
ions is not easy in general since the Morse indices of the nontrivial solu
tions could be high depending types of interaction terms. \nWhen the inte
raction forces between different components are very large\, we believe t
hat a relatively simpler structure we can see. Nevertheless\, a wide varie
ty of their asymptotic behavior we could imagine as various kinds of combi
nation for the interaction between components might produce various effect
s on the asymptotic behavior. The general study for elliptic systems with
large interaction forces is quite challenging.\nIn this talk\, I would lik
e to introduce my recent studies with collaborators on three components sy
stemsas basic steps to get general understanding for elliptic systems with
large interaction forces.\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edriss Titi (University of Cambridge)
DTSTART:20201116T140000Z
DTEND:20201116T150000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/11
DESCRIPTION:Title: The Inviscid Primitive Equations and the Effect of Rotation\nby
Edriss Titi (University of Cambridge) as part of "Partial Differential Eq
uations and Applications" Webinar\n\n\nAbstract\nLarge scale dynamics of t
he oceans and the atmosphere is governed by the primitive equations (PEs).
It is well-known that the three-dimensional viscous primitive equations a
re globally well-posed in Sobolev spaces. In this talk\, I will discuss th
e ill-posedness in Sobolev spaces\, the local well-posedness in the space
of analytic functions\, and the finite-time blowup of solutions to the thr
ee-dimensional inviscid PEs with rotation (Coriolis force). Eventually\, I
will also show\, in the case of ``well-prepared" analytic initial data\,
the regularizing effect of the Coriolis force by providing a lower bound f
or the life-span of the solutions which grows toward infinity with the rot
ation rate. The latter is achieved by a delicate analysis of a simple limi
t resonant system whose solution approximate the corresponding solution of
the 3D inviscid PEs with the same initial data.\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre-Emmanuel Jabin (University of Maryland)
DTSTART:20201123T140000Z
DTEND:20201123T150000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/12
DESCRIPTION:Title: Large stochastic systems of interacting particles\nby Pierre-Em
manuel Jabin (University of Maryland) as part of "Partial Differential Equ
ations and Applications" Webinar\n\n\nAbstract\nI will present some recent
results\, obtained with D. Bresch and Z. Wang\, on large stochastic many-
particle or multi-agent systems. Because such systems are conceptually sim
ple but exhibit a wide range of emerging macroscopic behaviors\, they are
now employed in a large variety of applications from Physics (plasmas\, ga
laxy formation...) to the Biosciences\, Economy\, Social Sciences.\n\nThe
number of agents or particles is typically quite large\, with 1020-1025 pa
rticles in many Physics settings for example and just as many equations. A
nalytical or numerical studies of such systems are potentially very comple
x leading to the key question as to whether it is possible to reduce this
complexity\, notably thanks to the notion of propagation of chaos (agents
remaining almost uncorrelated). \n\nTo derive this propagation of chaos\,
we have introduced a novel analytical method\, which led to the resolutio
n of two long-standing conjectures: \n\n- The quantitative derivation of t
he 2-dimensional incompressible Navier-Stokes system from the point vortic
es dynamics\; \n\n- The derivation of the mean-field limit for attractive
singular interactions such as in the Keller-Segel model for chemotaxis and
some Coulomb gases.\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose A. Carrillo (University of Oxford)
DTSTART:20201130T140000Z
DTEND:20201130T150000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/13
DESCRIPTION:Title: Nonlinear Aggregation-Diffusion Equations: Gradient Flows\, Free En
ergies and Phase Transitions\nby Jose A. Carrillo (University of Oxfor
d) as part of "Partial Differential Equations and Applications" Webinar\n\
n\nAbstract\nThe main goal of this talk is to discuss the state-of-the-art
in understanding the phenomena of phase transitions for a range of nonlin
ear Fokker-Planck equations with linear and nonlinear diffusion. They appe
ar as natural macroscopic PDE descriptions of the collective behavior of p
articles such as Cucker-Smale models for consensus\, the Keller Segel mode
l for chemotaxis\, and the Kuramoto model for synchronization. We will sho
w the existence of phase transitions in a variety of these models using th
e natural free energy of the system and their interpretation as natural gr
adient flow structure with respect to the Wasserstein distance in probabil
ity measures. We will discuss both theoretical aspects as well as numerica
l schemes and simulations keeping those properties at the discrete level.\
n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marie E. Rognes (Simula)
DTSTART:20201207T140000Z
DTEND:20201207T150000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/14
DESCRIPTION:Title: The brain's waterscape\nby Marie E. Rognes (Simula) as part of
"Partial Differential Equations and Applications" Webinar\n\n\nAbstract\nY
our brain has its own waterscape: whether you are reading or sleeping\, fl
uid flows around or through the brain tissue and clears waste in the proce
ss. These physiological processes are crucial for the well-being of the br
ain. In spite of their importance we understand them but little. Mathemati
cs and numerics could play a crucial role in gaining new insight. Indeed\,
medical doctors express an urgent need for modeling of water transport th
rough the brain\, to overcome limitations in traditional techniques. Surpr
isingly little attention has been paid to the numerics of the brain’s wa
terscape however\, and fundamental knowledge is missing. In this talk\, I
will discuss mathematical models and numerical methods for the brain's wat
erscape across scales - from viewing the brain as a poroelastic medium at
the macroscale and zooming in to studying electrical\, chemical and mechan
ical interactions between brain cells at the microscale.\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Susanna Terracini (Università di Torino)
DTSTART:20201026T140000Z
DTEND:20201026T150000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/15
DESCRIPTION:Title: Segregation\, interaction of species and related free boundary prob
lems\nby Susanna Terracini (Università di Torino) as part of "Partial
Differential Equations and Applications" Webinar\n\n\nAbstract\nReaction-
diffusion systems with strong interaction terms appear in many multi-spec
ies physical problems as well as in population dynamics\, chemistry and ma
terial science. The qualitative properties of the solutions and their limi
ting profiles in different regimes have been at the center of the communit
y's attention in recent years. A prototypical example appears when looking
for solitary wave solutions for Bose-Einstein condensates of two (or more
) different hyperfine states which overlap in space. Typically the forces
between particles in the same state are attractive while those between par
ticles in different states can be either attractive or repulsive. If the c
ondensates repel\, they eventually separate spatially giving rise to a fr
ee boundary. This phenomenon is called phase separation and has been descr
ibed in recent literature\, both physical and mathematical. \n\nOne of th
e most interesting problems researchers investigate is when different phas
es of matter\, populations\, or clusters exist in a single space (i.e. in
adjacent cells). Their interest focuses not only in how these different p
hases/populations/clusters interact with one another\, but also on the pro
perties of the boundaries separating them. The recent literature shows tha
t the walls separating the different phases are geometrically tractable su
rfaces\, as well as multiple junctions among them. This involves developin
g novel variational methods and geometric measure theory and free boundary
tools. Relevant connections have been established with optimal partition
problems involving spectral functionals. The classification of entire so
lutions and the geometric aspects of the nodal sets of solutions are of fu
ndamental importance as well. We intend to focus on the most recent develo
pment of the theory in connection with problems featuring anomalous diffus
ions\, long-range and non symmetric.\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanyan Li (Rutgers)
DTSTART:20201102T140000Z
DTEND:20201102T150000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/16
DESCRIPTION:Title: Gradient estimates for the insulated conductivity problem\nby Y
anyan Li (Rutgers) as part of "Partial Differential Equations and Applicat
ions" Webinar\n\n\nAbstract\nIn this talk\, we discuss the insulated condu
ctivity problem with multiple inclusions embedded in a bounded domain in n
-dimensional Euclidean space. The gradient of a solution may blow up as tw
o inclusions approach each other. The optimal blow up rate was known in di
mension n=2. It was not known whether the established upper bound of the b
low up rates in higher dimensions were optimal.\nWe answer this question b
y improving the previously known upper bound of the blow up rates in dimen
sion n>2.\nThis is a joint work with Zhuolun Yang.\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marie-Therese Wolfram (University of Warwick)
DTSTART:20201214T140000Z
DTEND:20201214T150000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/17
DESCRIPTION:Title: On mean-field models in pedestrian dynamics\nby Marie-Therese W
olfram (University of Warwick) as part of "Partial Differential Equations
and Applications" Webinar\n\n\nAbstract\nIn this talk I will start with a
general overview on mean-field models for pedestrian dynamics\, outlining
the challenges in the derivation and the analysis of the corresponding PDE
models. I will then illustrate how this continuum description can be used
to understand the effect of inflow and outflow rates as well as the geome
try on pedestrian density profiles. Finally I will present how the Bayesi
an framework can be used to identify parameters in mean field models and q
uantify uncertainty in those estimates using trajectory data.\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huyên Pham (Paris Diderot)
DTSTART:20210208T140000Z
DTEND:20210208T150000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/18
DESCRIPTION:by Huyên Pham (Paris Diderot) as part of "Partial Differentia
l Equations and Applications" Webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eitan Tadmor (University of Maryland)
DTSTART:20210215T140000Z
DTEND:20210215T150000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/19
DESCRIPTION:by Eitan Tadmor (University of Maryland) as part of "Partial D
ifferential Equations and Applications" Webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diogo Gomes (KAUST)
DTSTART:20210222T140000Z
DTEND:20210222T150000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/20
DESCRIPTION:by Diogo Gomes (KAUST) as part of "Partial Differential Equati
ons and Applications" Webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Melenk (TU Wien)
DTSTART:20210304T140000Z
DTEND:20210304T150000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/21
DESCRIPTION:Title: High order numerical methods for fractional diffusion in polygons\nby Markus Melenk (TU Wien) as part of "Partial Differential Equations
and Applications" Webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kanishka Perera (Florida Tech)
DTSTART:20210311T140000Z
DTEND:20210311T150000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/22
DESCRIPTION:Title: An abstract critical point theorem with applications to elliptic pr
oblems with combined nonlinearities\nby Kanishka Perera (Florida Tech)
as part of "Partial Differential Equations and Applications" Webinar\n\nA
bstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Mingione (Università di Parma)
DTSTART:20210318T140000Z
DTEND:20210318T150000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/23
DESCRIPTION:Title: Nonuniformly elliptic problems\nby Giuseppe Mingione (Universit
à di Parma) as part of "Partial Differential Equations and Applications"
Webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mouhamed Moustapha Fall (AIMS-Senegal)
DTSTART:20210325T140000Z
DTEND:20210325T150000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/24
DESCRIPTION:Title: Constant (nonlocal) Mean curvature surfaces\nby Mouhamed Mousta
pha Fall (AIMS-Senegal) as part of "Partial Differential Equations and App
lications" Webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Camillo De Lellis (IAS Princeton)
DTSTART:20210429T130000Z
DTEND:20210429T140000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/25
DESCRIPTION:Title: Flows of vector fields: classical and modern\nby Camillo De Lel
lis (IAS Princeton) as part of "Partial Differential Equations and Applica
tions" Webinar\n\n\nAbstract\nConsider a (possibly time-dependent) vector
field $v$ on the Euclidean space. The classical Cauchy-Lipschitz (also nam
ed Picard-Lindelöf) Theorem states that\, if the vector field $v$ is Lips
chitz in space\, for every initial datum $x$ there is a unique trajectory
$\\gamma$ starting at $x$ at time $0$ and solving the ODE $\\dot{\\gamma}
(t) = v (t\, \\gamma (t))$. The theorem looses its validity as soon as $v$
is slightly less regular. However\, if we bundle all trajectories into a
global map allowing $x$ to vary\, a celebrated theory put forward by DiPer
na and Lions in the 80es show that there is a unique such flow under very
reasonable conditions and for much less regular vector fields. A long-stan
ding open question is whether this theory is the byproduct of a stronger c
lassical result which ensures the uniqueness of trajectories for almost ev
ery initial datum. I will give a complete answer to the latter question an
d draw connections with partial differential equations\, harmonic analysis
\, probability theory and Gromov's $h$-principle.\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Tice (CMU)
DTSTART:20210506T130000Z
DTEND:20210506T140000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/26
DESCRIPTION:Title: Traveling wave solutions to the free boundary Navier-Stokes equatio
ns\nby Ian Tice (CMU) as part of "Partial Differential Equations and A
pplications" Webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Kühn (TU Munich)
DTSTART:20210513T130000Z
DTEND:20210513T140000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/27
DESCRIPTION:Title: Geometric Singular Perturbation Theory for Fast-Slow PDEs\nby C
hristian Kühn (TU Munich) as part of "Partial Differential Equations and
Applications" Webinar\n\n\nAbstract\nSystems with multiple time scales app
ear in a wide variety of applications. Yet\, their mathematical analysis i
s challenging already in the context of ODEs\, where about four decades we
re needed to develop a more comprehensive theory based upon invariant mani
folds\, desingularization\, variational equations\, and many other techniq
ues.\nYet\, for PDEs progress has been extremely slow due to many obstacle
s in generalizing several ODE methods. In my talk\, I shall report on two
recent advances for fast-slow PDEs\, namely the extension of slow manifold
theory for unbounded operators driving the slow variables\, and the desig
n of a blow-up method for PDEs\, where normal hyperbolicity is lost. This
is joint work with Maximilian Engel and Felix Hummel.\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hung Vinh Tran (University of Wisconsin Madison)
DTSTART:20210520T130000Z
DTEND:20210520T140000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/28
DESCRIPTION:Title: Large time behavior and large time profile of viscous Hamilton-Jaco
bi equations\nby Hung Vinh Tran (University of Wisconsin Madison) as p
art of "Partial Differential Equations and Applications" Webinar\n\n\nAbst
ract\nI will describe our recent results on large time behavior and large
time profile of viscous Hamilton-Jacobi equations in the periodic setting.
Here\, the diffusion matrix might be degenerate\, which makes the problem
more difficult and challenging. Based on joint works with Cagnetti\, Gome
s\, Mitake.\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi-Wang Shu (Brown University)
DTSTART:20210527T130000Z
DTEND:20210527T140000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/29
DESCRIPTION:Title: Stability of time discretizations for semi-discrete high order sche
mes for time-dependent PDEs\nby Chi-Wang Shu (Brown University) as par
t of "Partial Differential Equations and Applications" Webinar\n\n\nAbstra
ct\nIn scientific and engineering computing\, we encounter time-dependent
partial differential equations (PDEs) frequently. When designing high ord
er schemes for solving these time-dependent PDEs\, we often first develop
semi-discrete schemes paying attention only to spatial discretizations and
leaving time $t$ continuous. It is then important to have a high order t
ime discretization to main the stability properties of the semi-discrete s
chemes. In this talk we discuss several classes of high order time discre
tization\, including the strong stability preserving (SSP) time discretiza
tion\, which preserves strong stability from a stable spatial discretizati
on with Euler forward\, the implicit-explicit (IMEX) Runge-Kutta or multi-
step time marching\, which treats the more stiff term (e.g. diffusion term
in a convection-diffusion equation) implicitly and the less stiff term (e
.g. the convection term in such an equation) explicitly\, for which strong
stability can be proved under the condition that the time step is upper-b
ounded by a constant under suitable conditions\, and the explicit Runge-Ku
tta methods\, for which strong stability can be proved in many cases for s
emi-negative linear semi-discrete schemes. Numerical examples will be giv
en to demonstrate the performance of these schemes.\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Mazzucato (Penn State)
DTSTART:20210603T130000Z
DTEND:20210603T140000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/30
DESCRIPTION:Title: Direct and inverse problems for a model of dislocations in geophysi
cs\nby Anna Mazzucato (Penn State) as part of "Partial Differential Eq
uations and Applications" Webinar\n\n\nAbstract\nI will discuss a model fo
r dislocations in an elastic medium\, modeling faults in the Earth's crust
. The direct problem consists in solving a non-standard boundary value/int
erface problem for isotropic\, in-homogeneous linear elasticity with piece
wise Lipschitz Lame' parameters\, for which we prove well-posedness and a
double-layer potential representation for the solution if the coefficients
jumps only along the fault. The non-linear inverse problem consists in de
termining the fault surface and slip vector from displacement measurements
made at the surface. We prove uniqueness under some geometric conditions\
, using unique continuation results for systems.\nWe also establish shape
derivative formulas under infinitesimal movements of the fault and change
s in the slip. The application of the inverse problem is in fault monitor
ing and microseismicity. This is joint work with Andrea Aspri (Pavia Unive
rsity)\, Elena Beretta (Politechnico\, Milan & NYU-Abu Dhabi)\, and Maarte
n de Hoop (Rice).\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philipp Grohs (University of Vienna)
DTSTART:20210610T130000Z
DTEND:20210610T140000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/31
DESCRIPTION:Title: Deep Learning in Numerical Analysis\nby Philipp Grohs (Universi
ty of Vienna) as part of "Partial Differential Equations and Applications"
Webinar\n\n\nAbstract\nThe development of new classification and regressi
on algorithms based on deep neural networks coined Deep Learning have had
a dramatic impact in the areas of artificial intelligence\, machine learni
ng\, and data analysis. More recently\, these methods have been applied su
ccessfully to the numerical solution of partial differential equations (PD
Es). However\, a rigorous analysis of their potential and limitations is s
till largely open. In this talk we will survey recent results contributing
to such an analysis. In particular I will present recent empirical and th
eoretical results supporting the capability of Deep Learning based methods
to break the curse of dimensionality for several high dimensional PDEs\,
including nonlinear Black Scholes equations used in computational finance\
, Hamilton Jacobi Bellman equations used in optimal control\, and stationa
ry Schrödinger equations used in quantum chemistry. Despite these encoura
ging results\, it is still largely unclear for which problem classes a Dee
p Learning based ansatz can be beneficial. To this end I will\, in a secon
d part\, present recent work establishing fundamental limitations on the c
omputational efficiency of Deep Learning based numerical algorithms that\,
in particular\, confirm a previously empirically observed "theory-to-prac
tice gap".\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Apala Majumdar (University of Strathclyde)
DTSTART:20210617T130000Z
DTEND:20210617T140000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/32
DESCRIPTION:Title: PDE problems in the Landau-de Gennes theory for Nematic Liquid Crys
tals\nby Apala Majumdar (University of Strathclyde) as part of "Partia
l Differential Equations and Applications" Webinar\n\n\nAbstract\nNematic
liquid crystals are classical examples of partially ordered materials that
combine fluidity with the order of crystalline solids. Nematics have long
-range orientational order i.e. they are directional materials with specia
l directions\, referred to as directors. The Landau-de Gennes theory is on
e of the most celebrated and powerful continuum theories for nematic liqui
d crystals. In this talk\, we review the mathematical framework for the La
ndau-de Gennes theory with emphasis on the Landau-de Gennes free energy an
d the associated Euler-Lagrange equations\, which are typically a system o
f coupled\, nonlinear partial differential equations. We review some recen
t results for boundary-value problems in the Landau-de Gennes theory\, inc
luding results on the multiplicity\, defect sets and asymptotic analysis o
f energy-minimizing solutions. We also describe the physical relevance of
these solutions\, followed by case studies of applications in the physical
sciences and industry.\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoichiro Mori (University of Pennsylvania)
DTSTART:20210624T130000Z
DTEND:20210624T140000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/33
DESCRIPTION:Title: Analysis of the Dynamics of Immersed Elastic Filaments in Stokes Fl
ow\nby Yoichiro Mori (University of Pennsylvania) as part of "Partial
Differential Equations and Applications" Webinar\n\n\nAbstract\nWe conside
r the problem of an elastic filament immersed in a 2D or 3D Stokes fluid.
We first discuss the analysis of an immersed filament problem in a 2D Stok
es fluid (the Peskin problem). We prove well-posedness and immediate regul
arization of the elastic filament configuration and discuss criteria for g
lobal existence. We will then discuss the immersed filament problem in a 3
D Stokes fluid (the Slender Body problem). Here\, it has not even been cle
ar what the appropriate mathematical formulation of the problem should be.
We propose a mathematical formulation for the Slender Body problem and di
scuss well-posedness for the stationary version of this problem. Furthermo
re\, we prove that the Slender Body approximation\, introduced by Keller a
nd Rubinow in the 1980's and used widely in computation\, provides an appr
oximation to the Slender Body problem.\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrico Valdinoci (University of Western Australia)
DTSTART:20210923T130000Z
DTEND:20210923T140000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/34
DESCRIPTION:Title: Nonlocal minimal surfaces are generically sticky\nby Enrico Val
dinoci (University of Western Australia) as part of "Partial Differential
Equations and Applications" Webinar\n\n\nAbstract\nSurfaces which minimize
a nonlocal perimeter functional exhibit quite different behaviors than th
e ones minimizing the classical perimeter. Among these peculiar features\,
an interesting property\, which is also in contrast with the pattern prod
uced by the solutions of linear equations\, is given by the capacity\, and
the strong tendency\, of adhering at the boundary. We will discuss this p
henomenon and present some recent results.\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Quirós (Universidad Autónoma de Madrid)
DTSTART:20210930T130000Z
DTEND:20210930T140000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/35
DESCRIPTION:Title: Travelling-wave behaviour in problems with degenerate diffusion
\nby Fernando Quirós (Universidad Autónoma de Madrid) as part of "Partia
l Differential Equations and Applications" Webinar\n\n\nAbstract\nWe revie
w some recent results on the large-time behaviour of solutions to certain
reaction-diffusion equations involving a diffusion operator that degenerat
es at the level 0. Nonnegative solutions with compactly supported initial
data have a compact support for any later time\, so that the problem has a
free boundary whose asymptotic location one would like to determine.\n\nP
roblems in this family have a unique (up to translations) travelling wave
solution with a finite front. When the initial datum is bounded\, radially
symmetric and compactly supported\, we prove that solutions converging to
1 (which exist for all the reaction terms under consideration) do so by a
pproaching a translation of this unique traveling wave in the radial direc
tion\, but with a logarithmic correction in the position of the front when
the dimension is bigger than one. As a corollary we obtain the asymptotic
location of the free boundary and level sets in the non-radial case up to
an error term of size $O(1)$. A main technical tool of independent intere
st is an estimate for the flux.\n\nThis is a collaboration with Y. Du\, A.
Gárriz and M. Zhou.\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessio Figalli (ETH Zürich)
DTSTART:20211021T130000Z
DTEND:20211021T140000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/36
DESCRIPTION:Title: Free boundary regularity in the Stefan problem\nby Alessio Figa
lli (ETH Zürich) as part of "Partial Differential Equations and Applicati
ons" Webinar\n\n\nAbstract\nThe Stefan problem describes phase transitions
such as ice melting to water\, and it is among the most classical free bo
undary problems. It is well known that the free boundary consists of a smo
oth part (the regular part) and singular points. In this talk\, I will des
cribe a recent result with Ros-Oton and Serra\, where we analyze the singu
lar set in the Stefan problem and prove a series of fine results on its st
ructure.\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Helena Nussenzveig Lopes (Universidade Federal do Rio de Janeiro)
DTSTART:20211028T130000Z
DTEND:20211028T140000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/37
DESCRIPTION:Title: 2D Navier-Stokes equations on a bounded domain with holes and Navie
r friction boundary conditions\nby Helena Nussenzveig Lopes (Universid
ade Federal do Rio de Janeiro) as part of "Partial Differential Equations
and Applications" Webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Engelstein (University of Minnesota)
DTSTART:20211104T140000Z
DTEND:20211104T150000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/38
DESCRIPTION:Title: Generic Smoothness for the nodal sets of solutions to the Dirichlet
problem for Elliptic PDE\nby Max Engelstein (University of Minnesota)
as part of "Partial Differential Equations and Applications" Webinar\n\nA
bstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniela De Silva
DTSTART:20211111T140000Z
DTEND:20211111T150000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/39
DESCRIPTION:Title: Global minimizers to the one-phase free boundary problem\nby Da
niela De Silva as part of "Partial Differential Equations and Applications
" Webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henrik Shahgholian (Royal Institute of Technology)
DTSTART:20211118T140000Z
DTEND:20211118T150000Z
DTSTAMP:20260404T131153Z
UID:SNPDEA/40
DESCRIPTION:Title: A free boundary perspective on transmission and inverse scattering
problems\nby Henrik Shahgholian (Royal Institute of Technology) as par
t of "Partial Differential Equations and Applications" Webinar\n\nAbstract
: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SNPDEA/40/
END:VEVENT
END:VCALENDAR