Instantaneous shrinking in nonlinear diffusion-convection

B.H. Gilding, R. Kersner

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    25 Citations (Scopus)
    73 Downloads (Pure)

    Abstract

    The Cauchy problem for a nonlinear diffusion-convection equation is studied. The equation may be classified as being of degenerate parabolic type with one spatial derivative and a time derivative. It is shown that under certain conditions solutions of the initial-value problem exhibit instantaneous shrinking. This is to say, at any positive time the spatial support of the solution is bounded above, although the support of the initial data function is not. This is a phenomenon which is normally only associated with nonlinear diffusion with strong absorption. In conjunction, a previously unreported phenomenon is revealed. It is shown that for a certain class of initial data functions there is a critical positive time such that the support of the solution is unbounded above at any earlier time, whilst the opposite is the case at any later time.
    Original languageEnglish
    Pages (from-to)385-394
    Number of pages10
    JournalProceedings of the American Mathematical Society
    Volume109
    Issue number2
    DOIs
    Publication statusPublished - 1990

    Keywords

    • qualitative behavior
    • IR-74997
    • METIS-140639
    • Diffusion
    • Nonlinear degenerate parabolic equation
    • Convection

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