Travelling waves in nonlinear diffusion-convection-reaction


Gilding, B.H. and Kersner, R. (2001) Travelling waves in nonlinear diffusion-convection-reaction. [Report]

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Abstract: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.
Item Type:Report
Additional information:Imported from MEMORANDA
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Metis ID: 200352