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

    Fingerprint

    Monotone Method
    Advection-diffusion
    Global Attractivity
    Volterra Equation
    Existence and Uniqueness Results
    Lyapunov Functional
    Asymptotic Behavior of Solutions
    Volterra
    Advection
    Inhomogeneity
    Semilinear
    Diffusion equation
    Positive Solution
    Asymptotic Behavior
    Sufficient Conditions
    Interaction
    Standards

    Keywords

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

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Asymptotic behavior of solutions for semilinear volterra diffusion equations with spatial inhomogeneity and advection. / Yoshida, Yusuke; Yamada, Yoshio.

    In: Tokyo Journal of Mathematics, Vol. 39, No. 1, 01.06.2016, p. 271-292.

    Research output: Contribution to journalArticle

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