Connecting orbit structure of monotone solutions in the shadow system
type: Item
instance of: scholarly article
title: Connecting orbit structure of monotone solutions in the shadow system
zbMATH Open document ID: 0902.35058
author: Hiroshi Kokubu
author: K. Mischaikow
author: Yasumasa Nishiura
author: Hireo Oka
author: Takeshi Takaishi
published in: Journal of Differential Equations
publication date: 1998-01-26T00:00:00Z
full work available at URL: http://hdl.handle.net/2115/40186
review text: The authors study the dynamical system given by the following system of reaction-diffusion equations \[ {\partial u\over\partial t}= \varepsilon^2 {\partial^2u\over\partial x^2}+ f(u)- \xi,\quad {d\xi\over dt}= \int_I g(u,\xi)dx \] for \((t, x)\in [0,\infty)\times I\), where \(u\) satisfies the Neumann boundary condition on \([0,\infty)\times \partial I\). Here \(I= (0,1)\). The structure of the attractor (consisting of functions monotone in \(x\)) is investigated. The stability of equilibrium solutions and the connection orbits between them are classified.
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 37C70
zbMATH DE Number: 1109522
zbMATH Keywords: stability of equilibrium solutions
reviewed by: Shuichi Jimbo
MaRDI profile type: Publication
OpenAlex ID: W2026691120
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DOI: 10.1006/JDEQ.1997.3317
description: scientific article; zbMATH DE number 1109522