Travelling waves in nonlinear diffusion-convection reaction
type: Item
instance of: scholarly article
title: Travelling waves in nonlinear diffusion-convection reaction
zbMATH Open document ID: 1073.35002
author: Brian H. Gilding
author: Robert Kersner
published in: Progress in Nonlinear Differential Equations and Their Applications
publication date: 2004-11-23T00:00:00Z
review text: This book concerns a technique which can be used to determine whether or not a nonlinear second order scalar reaction convection diffusion equation admits a travelling wave solution and to investigate the properties of such a travelling. The method involves the study of an integral equation, and is an alternative to phase plane analysis. Due to this, Chapters 5 to 7 are then specifically concerned with the application of the integral equation theory to determine the existence of travelling wave solutions of particular reaction convection diffusion equations. In addition, in Chapter 10 particular attention is paid to equations in which the reaction term has a fixed sign, to equations in which the reaction term has on sign change, and, to equations with smooth coefficients. Finally, unbounded travelling wave solutions are considered in Chapters 11 and 12.
reviewed by: Abdolrahman Razani
Mathematics Subject Classification ID: 35-02
Mathematics Subject Classification ID: 35K35
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35Qxx
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 92C15
Mathematics Subject Classification ID: 92C20
zbMATH DE Number: 2117719
zbMATH Keywords: nonlinear diffusion
zbMATH Keywords: integral equation
zbMATH Keywords: unbounded travelling wave solution
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2117719