## 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*************************************************

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

gradients and small diffusions

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