Standing wave solutions for a Fisher type equation with a nonlocal convection
type: Item
instance of: scholarly article
title: Standing wave solutions for a Fisher type equation with a nonlocal convection
zbMATH Open document ID: 0634.35039
author: Masayasu Mimura
author: Kazutaka Ohara
published in: Hiroshima Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: The author considers the actual solvability of a nonlinear equation \(du_{xx}''-[(K*u)u]'+ku(1-u)=0.\) It is proved that there is no solution in C \(2(R)\cap L_ 1(R)\cap L_{\infty}(R)\) for kernels \(K(x)\in L_ 1(R)\), and that for some specific kernel \(K(x)\not\in L_ 1(R)\) there is a range of value of \(\int_{R}u dx\) over which such a solution exists.
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 4032212
zbMATH Keywords: stationary solitary wave solutions
zbMATH Keywords: nonlinear diffusion
zbMATH Keywords: existence
zbMATH Keywords: non- existence
zbMATH Keywords: solvability
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4032212