The effect of non-local convection on reaction-diffusion equations
type: Item
instance of: scholarly article
title: The effect of non-local convection on reaction-diffusion equations
zbMATH Open document ID: 0636.35041
published in: Hiroshima Mathematical Journal
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://projecteuclid.org/download/pdf_1/euclid.hmj/1206130067
review text: The equation (1) \(\partial u/\partial t=\partial /\partial x\{\partial u/\partial x-(K*u)u\}+\epsilon f(u)\) is investigated. K*u denotes the convolution with kernel \(K(x)=-r\) \((x>0)\) or \(+r\) \((x<0)\), where r is a positive constant. The author shows that if \(\epsilon >0\) is sufficiently small, the study of the existence and their stability of stationary solutions of (1) are reduced to investigate zeros and the sign of a derivative at each zero of some function F. He also investigates the effect of such a non-local convection on the behavior of solutions by using the function F.
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 4036299
zbMATH Keywords: reaction-diffusion equations
zbMATH Keywords: existence
zbMATH Keywords: stability
zbMATH Keywords: stationary solutions
zbMATH Keywords: non-local convection
author: Shin-Ichiro Ei
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4036299