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BEGIN:VEVENT
SUMMARY:Yaping Wu (Capital Normal University)
DTSTART:20200803T130000Z
DTEND:20200803T133000Z
DTSTAMP:20260404T041741Z
UID:BIRS_20w5205/1
DESCRIPTION:Title: The spectral stability of bacteria pulse wave for a Keller-Seg
el chemotactic model\nby Yaping Wu (Capital Normal University) as part
of BIRS workshop: Interfacial Phenomena in Reaction-Diffusion Systems\n\n
\nAbstract\nIn this talk we shall talk about our recent work on the spectr
al stability/instability of the whole family of explicit traveling waves $
(B(x-ct)\,S(x-ct))$ in some weighted spaces\, by applying detailed spect
ral analysis\, Evan's function method and numerical simulation. We shall a
lso talk about our work on the local well-posedness of solution for the or
iginal Keller-Segel model \\eqref{KS}.\n\nIt's a joint work with Yi Li\, Y
ong Li and Hao Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5205/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quentin Griette (University of Bordeaux)
DTSTART:20200803T134000Z
DTEND:20200803T141000Z
DTSTAMP:20260404T041741Z
UID:BIRS_20w5205/2
DESCRIPTION:Title: Sharp discontinuous traveling waves in a hyperbolic Keller–S
egel equation\nby Quentin Griette (University of Bordeaux) as part of
BIRS workshop: Interfacial Phenomena in Reaction-Diffusion Systems\n\n\nAb
stract\nThis talk concerns a hyperbolic model of cell-cell repulsion with
a dynamics in the population of cells. More precisely\, we consider a popu
lation of cells producing a field (the “pressure”) which induces a mot
ion of the cells following the opposite of the gradient. The field indicat
es the local density of population and we assume that cells try to avoid c
rowded areas and prefer locally empty spaces which are far away from the c
arrying capacity. We analyze the well-posedness property of the associated
Cauchy problem on the real line. We start from bounded initial conditions
and we consider some invariant properties of the initial conditions such
as the continuity\, smoothness and monotony. We also describe in detail th
e behavior of the level sets near the propagating boundary of the solution
and we find that an asymptotic jump is formed on the solution for a natur
al class of initial conditions. Finally\, we prove the existence of sharp
traveling waves for this model\, which are particular solutions traveling
at a constant speed\, and argue that sharp traveling waves are necessarily
discontinuous. This analysis is confirmed by numerical simulations of the
PDE problem. \n\nThis is a joint work with Xiaoming Fu and Pierre Magal.\
n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5205/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xing Liang (University of Science and Technology of China)
DTSTART:20200803T142000Z
DTEND:20200803T145000Z
DTSTAMP:20260404T041741Z
UID:BIRS_20w5205/3
DESCRIPTION:Title: Spreading speeds of nonlocal diffusion KPP equations\nby X
ing Liang (University of Science and Technology of China) as part of BIRS
workshop: Interfacial Phenomena in Reaction-Diffusion Systems\n\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5205/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Giletti (University of Lorraine)
DTSTART:20200804T130000Z
DTEND:20200804T133000Z
DTSTAMP:20260404T041741Z
UID:BIRS_20w5205/4
DESCRIPTION:Title: Propagating terraces in multidimensional and spatially periodi
c domains\nby Thomas Giletti (University of Lorraine) as part of BIRS
workshop: Interfacial Phenomena in Reaction-Diffusion Systems\n\n\nAbstrac
t\nThis talk will be devoted to the existence of pulsating travelling fron
t solutions for spatially periodic heterogeneous reaction-diffusion equati
ons in arbitrary dimension\, in the multistable case. In general\, the not
ion of a single front is not sufficient to understand the dynamics of solu
tions\, and we instead observe the appearance of a so-called propagating t
errace. This roughly refers to a finite family of stacked fronts connectin
g intermediate stable steady states and whose speeds are ordered. Surprisi
ngly\, for a given equation\, the shape of this terrace (i.e.\, the involv
ed intermediate steady states or even their number) may depend on the dire
ction of the propagation. This in turn raises some difficulties in the spr
eading shape of solutions of the evolution problem. The presented results
come from a series of collaborations with W. Ding\, A. Ducrot\, H. Matano
and L. Rossi.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5205/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nao Hamamuki (Hokkaido University)
DTSTART:20200804T133000Z
DTEND:20200804T140000Z
DTSTAMP:20260404T041741Z
UID:BIRS_20w5205/5
DESCRIPTION:Title: Asymptotic behavior of solutions to level-set mean curvature f
low equations with discontinuous source terms\nby Nao Hamamuki (Hokkai
do University) as part of BIRS workshop: Interfacial Phenomena in Reaction
-Diffusion Systems\n\n\nAbstract\nMotivated by the two-dimensional nucleat
ion of crystal growth\,\nwe consider the initial-value problem of the leve
l-set mean curvature flow equation with discontinuous source terms.\n\nWe
discuss uniqueness and existence of viscosity solutions and study the asym
ptotic shape of solutions. Applying the game-theoretic interpretation for
this problem\, we also study the asymptotic speed of solutions.\n\nThis ta
lk is based on a joint work with K. Misu (Hokkaido University).\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5205/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Nordmann (University of Tel-Aviv)
DTSTART:20200804T140000Z
DTEND:20200804T143000Z
DTSTAMP:20260404T041741Z
UID:BIRS_20w5205/6
DESCRIPTION:Title: The symmetry of stable solutions of semilinear elliptic equati
ons\nby Samuel Nordmann (University of Tel-Aviv) as part of BIRS works
hop: Interfacial Phenomena in Reaction-Diffusion Systems\n\n\nAbstract\nCo
nsider a general semilinear elliptic equation with Neumann boundary condit
ions. A seminal result of Casten\, Holland (1978) and Matano (1979) states
that\, if the domain is convex and bounded\, any stable solution is const
ant. In this talk\, we will investigate whether this classification result
extends to convex unbounded domains\, or to some non-convex domains. Thes
e questions involve the geometry of the domain in a rather intricate way.
In particular\, our results recover and extend some classical results on D
e Giorgi's conjecture about the classification of stable solutions of the
Allen-Cahn equation in $R^n$.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5205/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cole Graham (Stanford University)
DTSTART:20200804T143000Z
DTEND:20200804T150000Z
DTSTAMP:20260404T041741Z
UID:BIRS_20w5205/7
DESCRIPTION:Title: Reaction-diffusion equations in the half-space\nby Cole Gr
aham (Stanford University) as part of BIRS workshop: Interfacial Phenomena
in Reaction-Diffusion Systems\n\n\nAbstract\nThe interplay between reacti
on-diffusion evolution and spatial boundary has received a great deal of r
ecent attention. In this talk\, we consider an essential example: reaction
-diffusion equations in the half-space. Using the maximum principle and th
e sliding method\, we handle a host of reactions (monostable\, ignition\,
and bistable) under a wide class of boundary conditions (Dirichlet and Rob
in). We consider the existence and uniqueness of steady states\, the asymp
totic speed of propagation\, and the existence of traveling waves. This is
joint work with Henri Berestycki.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5205/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryunosuke Mori (Meiji University)
DTSTART:20200805T130000Z
DTEND:20200805T133000Z
DTSTAMP:20260404T041741Z
UID:BIRS_20w5205/8
DESCRIPTION:Title: Mathematical Analysis of a Reaction-Diffusion Model for Neolit
hic Transition in Europe\nby Ryunosuke Mori (Meiji University) as part
of BIRS workshop: Interfacial Phenomena in Reaction-Diffusion Systems\n\n
\nAbstract\nIn 1996\, Aoki\, Shida and Shigesada proposed a three-componen
t reaction-diffusion model describing the spread of the early farming duri
ng the New Stone Age. By numerical simulations and some formal linearizati
on arguments\, they concluded that there are four different types of sprea
ding behaviors depending on the parameter values.\n\nIn this talk\, we giv
e theoretical justification to all of the four types of spreading behavior
s observed by Aoki et al. We also investigate the case where the motility
of the hunter-gatherers is not equal to that of the farmers\, which is not
discussed in the paper of Aoki et al.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5205/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chang-Hong Wu (National Chiao Tung University)
DTSTART:20200805T134000Z
DTEND:20200805T141000Z
DTSTAMP:20260404T041741Z
UID:BIRS_20w5205/9
DESCRIPTION:Title: Wave Propagation in Two-Species Strong Competition Models\
nby Chang-Hong Wu (National Chiao Tung University) as part of BIRS worksho
p: Interfacial Phenomena in Reaction-Diffusion Systems\n\n\nAbstract\nWave
propagation for the two-species Lotka-Volterra competition models has bee
n studied widely. In this talk\, we shall focus on the bistable waves and
discuss some recent progress.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5205/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wenxian Shen (Auburn University)
DTSTART:20200805T143000Z
DTEND:20200805T150000Z
DTSTAMP:20260404T041741Z
UID:BIRS_20w5205/10
DESCRIPTION:Title: Can chemotaxis speed up or slow down the spatial spreading in
parabolic-elliptic Keller-Segel systems with logistic source?\nby Wen
xian Shen (Auburn University) as part of BIRS workshop: Interfacial Phenom
ena in Reaction-Diffusion Systems\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5205/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masahiko Shimojo (Okayama University of Sciences)
DTSTART:20200806T130000Z
DTEND:20200806T133000Z
DTSTAMP:20260404T041741Z
UID:BIRS_20w5205/11
DESCRIPTION:Title: Convergence to traveling wave for the logarithmic diffusion e
quation with reaction term\nby Masahiko Shimojo (Okayama University of
Sciences) as part of BIRS workshop: Interfacial Phenomena in Reaction-Dif
fusion Systems\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5205/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maolin Zhou (Nankai University)
DTSTART:20200806T133000Z
DTEND:20200806T140000Z
DTSTAMP:20260404T041741Z
UID:BIRS_20w5205/12
DESCRIPTION:Title: The principal eigenvalue problem for some second order ellipt
ic and parabolic operators with large advection\nby Maolin Zhou (Nanka
i University) as part of BIRS workshop: Interfacial Phenomena in Reaction-
Diffusion Systems\n\n\nAbstract\nIn this talk\, we will show some recent r
esults about the limit problem of the principal eigenvalue for some second
elliptic and parabolic operators in one dimensional space when the advect
ion coefficient converges to infinity. It has some applications to the exi
stence and stability of solutions of single equations and systems. This is
a joint work with Shuang Liu\, Yuan Lou and Rui Peng.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5205/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harunori Monobe (Okayama University)
DTSTART:20200806T140000Z
DTEND:20200806T143000Z
DTSTAMP:20260404T041741Z
UID:BIRS_20w5205/13
DESCRIPTION:Title: Fast reaction limit of three-components reaction-diffusion sy
stems and free boundary problems describing population dynamics\nby Ha
runori Monobe (Okayama University) as part of BIRS workshop: Interfacial P
henomena in Reaction-Diffusion Systems\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5205/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Léo Girardin (University of Paris-Sud)
DTSTART:20200806T143000Z
DTEND:20200806T150000Z
DTSTAMP:20260404T041741Z
UID:BIRS_20w5205/14
DESCRIPTION:Title: Strong competition limit\, traveling waves and best dispersal
strategy for Lotka-Volterra competitive systems\nby Léo Girardin (Un
iversity of Paris-Sud) as part of BIRS workshop: Interfacial Phenomena in
Reaction-Diffusion Systems\n\n\nAbstract\nIn this talk\, I will present an
ongoing work in collaboration with\nDanielle Hilhorst about the singular
limit of a large class of\nstrongly coupled\, strongly competitive two-spe
cies reaction--diffusion \nsystems. Particular cases are the standard Lotk
a--Volterra system\, the\nPotts--Petrovskii cross-taxis system and the SKT
cross-diffusion system. \nWe focus on the singular limit of traveling wav
es and use the sign of\nthe wave speed as a criterion to compare dispersal
--growth strategies.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5205/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Michel Roquejoffre (Universite Paul Sabatier)
DTSTART:20200807T130000Z
DTEND:20200807T133000Z
DTSTAMP:20260404T041741Z
UID:BIRS_20w5205/15
DESCRIPTION:Title: Properties of a free boundary driven by a line of fast diffus
ion\nby Jean-Michel Roquejoffre (Universite Paul Sabatier) as part of
BIRS workshop: Interfacial Phenomena in Reaction-Diffusion Systems\n\n\nAb
stract\nThe situation is the following: a line\, having a strong diffusion
on its own\,\nexchanges mass with the half plane below\, supposed to be a
reactive medium. A front propagates\nboth on the line and below\, and one
wishes to describe its shape. This setting was proposed\n(collaboration w
ith H. Berestycki and L. Rossi) as a model of how biological invasions can
be\nenhanced by transportation networks.\n\nNumerical simulations\, due t
o A.-C. Coulon\, reveal an a priori surprising phenomenon:\nthe solution i
s not monotone in the direction orthogonal to the line. We will try to\nun
derstand this feature in the particular case of a free boundary problem th
at can be\nobtained as a limiting case of the original reaction-diffusion
system\, amd discuss\nfurther features of the free boundary\, such as its
shape at infinity\, or what happens when the\ndiffusion on the line become
s infinite.\n\nJoint work with L. Caffarelli.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5205/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Changfeng Gui (University of Texas at San Antonio)
DTSTART:20200807T134000Z
DTEND:20200807T141000Z
DTSTAMP:20260404T041741Z
UID:BIRS_20w5205/16
DESCRIPTION:Title: Propagation acceleration in reaction diffusion equations with
a fractional Laplacian\nby Changfeng Gui (University of Texas at San
Antonio) as part of BIRS workshop: Interfacial Phenomena in Reaction-Diffu
sion Systems\n\n\nAbstract\nIn this talk\, I will present recent results
on the propagation speed in a reaction diffusion system with an anomalou
s Levy process diffusion\, modeled by a nonlocal equation with a fracti
onal Laplacian and a generalized KPP type monostable nonlinearity. Given
a typical Heavy side initial datum\, we show that the speed of interfac
e propagation displays an algebraic rate behavior in time\, in contrast
to the known linear rate in the classical model of Brownian motion and
the exponential rate in the KPP model with the anomalous diffusion\, and
depends on the sensitive balance between the anomaly of the diffusion proc
ess and the strength of monostable reaction. In particular\, for the
combustion model with\na fractional Laplacian $(-\\Delta)^{s}$\, we show
that the speed of propagation transits continuously from being linear i
n time\, when a traveling wave solution exists for $s \\in (1/2\, 1)$\,
to being algebraic in time with a power reciprocal to $2s$\, when no tra
veling wave solution exists for $s \\in (0\, 1/2)$.\n\n The talk is bas
ed on a joint work with Jerome Coville and Mingfeng Zhao.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5205/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sigurd Angenent (University of Wisconsin)
DTSTART:20200807T142000Z
DTEND:20200807T145000Z
DTSTAMP:20260404T041741Z
UID:BIRS_20w5205/17
DESCRIPTION:Title: Dynamics of convex mean curvature flow\nby Sigurd Angenen
t (University of Wisconsin) as part of BIRS workshop: Interfacial Phenomen
a in Reaction-Diffusion Systems\n\n\nAbstract\nMean Curvature Flow defines
a gradient-like dynamical system on the space of convex hypersurfaces. I
will discuss what is known about the fixed points and connecting orbits o
f this flow.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS_20w5205/17/
END:VEVENT
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