偏微分方程式セミナー: Dynamics of localized patterns for the equation with nonlocal effects, 祐川 翼 氏, 石井 宙志 氏

開催日時

2019年11月22日 16時 30分 ～ 2019年11月22日 18時 00分

場所

北海道大学理学部3号館3-309室

講演者

祐川 翼 氏 (北海道大学)、石井 宙志 氏 (北海道大学)

祐川 翼 氏 (16:30 ～ 17:15)

題目: Standing pulse solutions for linear mass conserved reaction-diffusion system

概要:
In this talk, we consider a linear reaction diffusion system with mass conservation. This system come from the model equations for ‘Cell polarity’, which is biological phenomenon, and it is important problem that which pulse-like stationary solution exists or not. We will show that a pulse-like stationary solution exists under some conditions for reaction terms. To prove this, we use the fact the stationary problem is equivalent to a linear integro-differential equation. As time allows, we explain the relation between diffusion coefficients and stationary solution. This talk is based on a joint work with Sungrim Seirin Lee (Hiroshima University), Tomohiro Nakahara (Hiroshima University), Hiroshi Ishii (Hokkaido University) and Shin-Ichiro Ei (Hokkaido University).

石井 宙志 氏 (17:15 ～ 18:00)

題目: Existence of traveling waves to a nonlocal scalar equation with sign-changing kernel

概要:
In this talk, we address the existence of traveling wave solutions connecting two constant states to a nonlocal scalar equation with sign-changing kernel. A typical example of such kernel in the neural fields is the Mexican hat type function. We first introduce a new notion of upper-lower-solution for the equation of wave profile for a given wave speed. Then, we construct two different pairs of upper-lower-solutions and use Schauder’s fixed point theorem to obtain traveling waves for a continuum of wave speeds under some assumptions. Finally, we analyze wave profiles by showing the limit of the both-hand tails. This talk is based on a joint work with Shin-Ichiro Ei (Hokkaido University), Jong-Shenq Guo (Tamkang University) and Chin-Chin Wu (National Chung Hsing University).

世話人：黒田 紘敏、浜向 直