On logistic diffusion equations with nonlocal interaction terms

Yoshio Yamada

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    This paper is concerned with logistic diffusion equations with nonlocal interaction terms appearing in population biology. We intend to study effects of nonlocal terms and discuss the similarity and difference between local problems and nonlocal problems. Mainly, the stationary problem is investigated for a certain class of nonlocal terms. A constructive approach is proposed to look for positive stationary solutions and the unique existence of such a positive solution is established. The analysis of stationary solutions depends on the spectrum for the linearized operator around the stationary solution. However, the linearized operator contains a nonlocal term which makes the spectral analysis delicate and difficult. Putting some additional assumptions we will derive the asymptotic stability of the unique positive solution and, furthermore, its global attractivity. Finally, it will be seen that some arguments are valid to show the unique existence of a positive stationary solution for a considerably general class of nonlocal terms.

    Original languageEnglish
    Pages (from-to)51-62
    Number of pages12
    JournalNonlinear Analysis, Theory, Methods and Applications
    Volume118
    DOIs
    Publication statusPublished - 2015

    Fingerprint

    Nonlocal Interactions
    Logistic Equation
    Diffusion equation
    Logistics
    Stationary Solutions
    Term
    Asymptotic stability
    Spectrum analysis
    Positive Solution
    Nonlocal Problems
    Global Attractivity
    Operator
    Spectral Analysis
    Asymptotic Stability
    Biology
    Valid

    Keywords

    • Global attractivity
    • Logistic diffusion equation
    • Nonlocal problem
    • Stability
    • Stationary solution

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this

    On logistic diffusion equations with nonlocal interaction terms. / Yamada, Yoshio.

    In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 118, 2015, p. 51-62.

    Research output: Contribution to journalArticle

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