Traveling front solutions in nonlinear diffusion degenerate Fisher-KPP and Nagumo equations via the Conley index
type: Item
instance of: scholarly article
title: Traveling front solutions in nonlinear diffusion degenerate Fisher-KPP and Nagumo equations via the Conley index
zbMATH Open document ID: 1213.35168
author: Fatiha El Adnani
author: Hamad Talibi Alaoui
published in: Topological Methods in Nonlinear Analysis
publication date: 2010-10-01T00:00:00Z
review text: In the reaction diffusion equation \[ {\partial u\over \partial t}={\partial \over \partial x}\left(K(u){\partial u\over \partial x}\right)+F(u) \quad\text{for } x\in \mathbb{R},\;t\geq 0, \] let \(u(x,0)=u_0(x)\) with \(0\leq u_0(x)\leq 1\) for all \(x\in \mathbb{R}\). The density coefficient \(K\) and the reaction function \(F\) are assumed to satisfy certain smoothness and positivity conditions on the interval \([0,1]\). Two cases are considered: the degenerate generalized Fisher-KPP equation in which both \(F\)and \(K\) vanish at 0 and 1, and the degenerate generalized Nagumo equation in which both \(F\) and \(K\) also vanish at some \(\alpha \in (0,1)\). The authors use the Conley index theory to show that in each case, there exist traveling front solutions that connect the zeros of \(F\) (and \(K\)).
reviewed by: Yaping Liu
Mathematics Subject Classification ID: 35C07
Mathematics Subject Classification ID: 35A18
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K59
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 5794097
zbMATH Keywords: connected simple systems
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5794097