Blowup in a partial differential equation with conserved first integral

Chris Budd, Bill Dold, Andrew Stuart

    Research output: Contribution to journalArticlepeer-review

    Abstract

    A reaction-diffusion equation with a nonlocal term is studied. The nonlocal term acts to conserve the spatial integral of the unknown function as time evolves. Such equations give insight into biological and chemical problems where conservation properties predominate. The aim of the paper is to understand how the conservation property affects the nature of blowup. The equation studied has a trivial steady solution that is proved to be stable. Existence of nontrivial steady solutions is proved, and their instability established numerically. Blowup is proved for sufficiently large initial data by using a comparison principle in Fourier space. The nature of the blowup is investigated by a combination of asymptotic and numerical calculations.
    Original languageEnglish
    Pages (from-to)718-742
    Number of pages24
    JournalSIAM JOURNAL ON APPLIED MATHEMATICS
    Volume53
    Issue number3
    Publication statusPublished - Jun 1993

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