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

Shanbing Li, Yoshio Yamada

    Research output: Contribution to journalArticle

    5 Citations (Scopus)


    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
    Issue number1
    Publication statusPublished - 2018 May 1



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

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

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