Travelling waves in nonlinear diffusion-convection-reaction

B.H. Gilding, R. Kersner

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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.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherNumerical Analysis and Computational Mechanics (NACM)
    Number of pages197
    ISBN (Print)0169-2690
    Publication statusPublished - 2001

    Publication series

    NameMemorandum Faculteit TW
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1585
    ISSN (Print)0169-2690

    Keywords

    • METIS-200352
    • MSC-80A25
    • MSC-92D25
    • MSC-76R99
    • MSC-35K65
    • MSC-35K57
    • MSC-35K55
    • EWI-3405
    • IR-65772

    Cite this

    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).