The study of travelling waves or fronts has become an essential part of the mathematical analysis of nonlinear diffusion-convection-reaction processes. Whether or not a nonlinear second-order scalar reaction-convection-diffusion equation admits a travelling-wave solution can be determined by the study of a singular nonlinear integral equation. This article is devoted to demonstrating how this correspondence unifies and generalizes previous results on the occurrence of travelling-wave solutions of such partial differential equations. The detailed comparison with earlier results simultaneously provides a survey of the topic. It covers travelling-wave solutions of generalizations of the Fisher, Newell-Whitehead, Zeldovich, KPP and Nagumo equations, the Burgers and nonlinear Fokker-Planck equations, and extensions of the porous media equation.
|Place of Publication||Enschede|
|Publisher||Numerical Analysis and Computational Mechanics (NACM)|
|Number of pages||197|
|Publication status||Published - 2001|
|Name||Memorandum Faculteit TW|
|Publisher||Department of Applied Mathematics, University of Twente|
Gilding, B. H., & Kersner, R. (2001). Travelling waves in nonlinear diffusion-convection-reaction. (Memorandum Faculteit TW; No. 1585). Enschede: Numerical Analysis and Computational Mechanics (NACM).