Effect of cross-diffusion in the diffusion prey-predator model with a protection zone II

Shanbing Li, Yoshio Yamada

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    In the current paper, we continue the mathematical analysis studied in Li and Wu (2017) [15] and Oeda (2011) [22], and further study the effect of cross-diffusion for the predator on the stationary problem. The existence of positive solutions is first established by the bifurcation theory. We next discuss the limiting behavior of positive solutions when the intrinsic growth rate of the predator species tends to infinity. Moreover, as the prevention coefficient tends to infinity, we obtain two shadow systems and give the complete limiting characterization of positive solutions.

    Original languageEnglish
    Pages (from-to)971-992
    Number of pages22
    JournalJournal of Mathematical Analysis and Applications
    Volume461
    Issue number1
    DOIs
    Publication statusPublished - 2018 May 1

    Fingerprint

    Prey-predator Model
    Cross-diffusion
    Diffusion Model
    Predator
    Positive Solution
    Infinity
    Tend
    Bifurcation Theory
    Limiting Behavior
    Existence of Positive Solutions
    Mathematical Analysis
    Continue
    Limiting
    Coefficient

    Keywords

    • Coexistence solution
    • Cross-diffusion
    • Limiting behavior
    • Protection zone
    • Shadow system

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this

    Effect of cross-diffusion in the diffusion prey-predator model with a protection zone II. / Li, Shanbing; Yamada, Yoshio.

    In: Journal of Mathematical Analysis and Applications, Vol. 461, No. 1, 01.05.2018, p. 971-992.

    Research output: Contribution to journalArticle

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