PDE Seminar (2019/11/22): Dynamics of localized patterns for the equation with nonlocal effects
 Date

20191122 16:30 
20191122 18:00
 Place
 Faculty of Science Building #3, Room 309

Speaker/Organizer
 Tsubasa Sukekawa (Hokkaido University), Hiroshi Ishii (Hokkaido University)

 • Tsubasa Sukekawa (16:3017:15)
Title:
Standing pulse solutions for linear mass conserved reactiondiffusion system
Abstract:
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 pulselike stationary solution exists or not. We will show that a pulselike stationary solution exists under some conditions for reaction terms. To prove this, we use the fact the stationary problem is equivalent to a linear integrodifferential 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 ShinIchiro Ei (Hokkaido University).
• Hiroshi Ishii (17:1518:00)
Title:
Existence of traveling waves to a nonlocal scalar equation with signchanging kernel
Abstract:
In this talk, we address the existence of traveling wave solutions connecting two constant states to a nonlocal scalar equation with signchanging kernel. A typical example of such kernel in the neural ﬁelds is the Mexican hat type function. We ﬁrst introduce a new notion of upperlowersolution for the equation of wave proﬁle for a given wave speed. Then, we construct two different pairs of upperlowersolutions 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 bothhand tails. This talk is based on a joint work with ShinIchiro Ei (Hokkaido University), JongShenq Guo (Tamkang University) and ChinChin Wu (National Chung Hsing University).