## Mini Workshop of Dynamics of localized patterns for reaction-diffusion systems and related topics

Date
2019-8-9 10:00 - 2019-8-9 16:00
Place
Science Bldg. 3, 3F room 309
Organizer
Shin-Ichiro Ei

Speakers:
Chueh-Hsin Chang(Tunghai University, Taiwan)

Po-Chih Huang(National Chung Cheng University, Taiwan)

Chih-Chiang Huang(National Taiwan University, Taiwan)

Kohta Oono(Hokkaido University)

Mamoru Okamoto(Hokkaido University)

Hiroshi Ishii(Hokkaido University)

Tsubasa Sukekawa(Hokkaido University)

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Program:
Mini Workshop of
Dynamics of localized patterns for reaction-diffusion systems and related topics

Date: 9th Aug. 10:00 - 16:00
Venue: Science Building 3, 3F room 309

10:00 - 10:40
Chueh-Hsin Chang, Tunghai University (Taiwan)
The stability of traveling wave solutions for a diffusive competition system of three species

10:40 - 11:20
Mamoru Okamoto, Hokkaido University, 岡本 守, 北海道大学
Non-trivial traveling wave solution of a
particle-reaction-diffusion equation

11:30 - 12:10
Po-Chih Huang, National Chung Cheng University (Taiwan)
The traveling pulse of Keller-Segel system with nonlinear chemical gradients and small diffusions

13:40 - 14:00
Hiroshi Ishii, Hokkaido University, 石井 宙志, 北海道大学
Existence of traveling waves to a nonlocal scalar equation with
sign-changing kernel
14:00 - 14:20
Tsubasa Sukekawa, Hokkaido University, 祐川 翼, 北海道大学
Stable standing pulse solutions for linear mass conserved reaction
diffusion system

14:20 - 15:00
Chih-Chiang Huang, National Taiwan University (Taiwan)
Traveling waves for the FitzHugh-Naumo system in a cylinder

15:10 - 15:50
Kota Ohno, Hokkaido University 大野 航太, 北海道大学
Global feedback to coupled oscillator and reaction-diffusion system with the Belousov-Zhabotinsky reaction
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Abstract:

Chueh-Hsin Chang:
Title:
The stability of traveling wave solutions for
a diffusive competition system of three species
Abstract:
In this talk, we study a three species competition systems
in which the existence and
stability of the monotone wave fronts can be obtained
by using the techniques of sup-sub-solutions
and the spectral analysis of linearized operators.

Mamoru Okamoto, 岡本守:
Title:
Non-trivial traveling wave solution of a
particle-reaction-diffusion equation.
Abstract :
A particle-reaction-diffusion equation, which is a complex of ODE and
PDE,
is studied as a model of a self-propelled objects. The preceding study
shows the equation has an non-trivial traveling wave solution
numerically
and experimentally, but the solution seems to be against the known
mechanism of such a self-propullsion.
We show the sufficient condition for existence and non-existence of the
solution, and clarify the gap of the equation and the mechanism.

Po-Chih Huang:
Title:
The traveling pulse of Keller-Segel system with nonlinear chemical
Abstract:
We consider the Keller-Segel system with nonlinear chemical gradient
and small cell diffusion. The existence of the traveling pulses is
established by the geometric singular perturbation theory and
trapping regions. We also consider the linear instability of
these pulses by the spectral analysis of the linearized operators.

Hiroshi Ishii, 石井宙志:
Title :
Existence of traveling waves to a nonlocal scalar equation with
sign-changing kernel
Abstract :
In this talk, we will present about that the existence of traveling wave
solutions connecting two constant states to a nonlocal scalar equation
with
sign-changing kernel.
We introduce a new notion of upper-lower-solution for the equation of
wave
profile for a given wave speed.
And we show that the existence of nonnegative traveling waves connecting
the unstable state and the stable state for wave speeds large enough.

Tsubasa Sukekawa, 祐川 翼:
Title:
Stable standing pulse solutions for linear mass conserved reaction
diffusion system.
Abstract:
In this talk, we shall report our recent results on
the mathematical analysis to the model equation
for a biological problem. The equation is a linear mass
conserved reaction diffusion system with periodic
boundary condition. We consider the existence and
stability of standing pulse solutions for our equation
under some conditions related to the biological backgrounds.

Chih-Chiang Huang:
Title:
Traveling waves for the FitzHugh-Naumo system in a cylinder
Abstract:
In this talk, I would like to study the FitzHugh-Naumo system (FHN) with
monostable and bistable nonlinearity, respectively. Steady states of
(FHN)
in a bounded domain and traveling waves of (FHN) in a cylinder also are
investegated. Such a construction of the traveling wave is based on a
varational method.

Kota Ohno, 大野 航太:
Title
Global feedback to coupled oscillator and reaction-diffusion system with
the Belousov-Zhabotinsky reaction
Abstract
In the Belousov-Zhabotinsky reaction system,
we can observe characteristic behavior with
global feedback. In this study, we investigated coupled
oscillator and reaction-diffusion system
to clarify this behavior theoretically and experimentally.

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Supported by
Department of Mathematics, Hokkaido University
Research Center of Mathematics for Social Creativity, Hokkaido University