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

開催日時

2019年8月9日 10時 00分 ～ 2019年8月9日 16時 00分

場所

理学部３号館３－３０９大講義室

主催者

栄　伸一郎（北海道大学）

Speakers:

Chueh-Hsin Chang(Tunghai University, Taiwan)
Po-Chih Huang(National Chung Cheng University, Taiwan)
Chih-Chiang Huang(National Taiwan University, Taiwan)
大野 航太（北海道大学）
岡本 守（北海道大学）
石井 宙志（北海道大学）
祐川 翼（北海道大学）

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.

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