Asymptotic behavior of solutions for semilinear volterra diffusion equations with spatial inhomogeneity and advection

Yusuke Yoshida, Yoshio Yamada

    Research output: Contribution to journalArticle

    Abstract

    This paper is concerned with semilinear Volterra diffusion equations with spatial inhomogeneity and advection. We intend to study the effects of interaction among diffusion, advection and Volterra integral under spatially inhomogeneous environments. Since the existence and uniqueness result of global-in-time solutions can be proved in the standard manner, our main interest is to study their asymptotic behavior as t → ∞. For this purpose, we study the related stationary problem by the monotone method and establish some sufficient conditions on the existence of a unique positive solution. Its global attractivity is also studied with use of a suitable Lyapunov functional.

    Original languageEnglish
    Pages (from-to)271-292
    Number of pages22
    JournalTokyo Journal of Mathematics
    Volume39
    Issue number1
    Publication statusPublished - 2016 Jun 1

    Keywords

    • Advection
    • Global attractivity
    • Logistic equation
    • Lyapunov functional
    • Spatial inhomogeneity
    • Volterra diffusion equation

    ASJC Scopus subject areas

    • Mathematics(all)

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