Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with weak cross-diffusion

Y. S. Choi, Roger Lui, Yoshio Yamada

    Research output: Contribution to journalArticle

    46 Citations (Scopus)

    Abstract

    The Shigesada-Kawasaki-Teramoto model is a generalization of the classical Lotka-Volterra competition model for which the competing species undergo both diffusion, self-diffusion and cross-diffusion. Very few mathematical results are known for this model, especially in higher space dimensions. In this paper, we shall prove global existence of strong solutions in any space dimension for this model when the cross-diffusion coefficient in the first species is sufficiently small and when there is no self-diffusion or cross-diffusion in the second species.

    Original languageEnglish
    Pages (from-to)1193-1200
    Number of pages8
    JournalDiscrete and Continuous Dynamical Systems
    Volume9
    Issue number5
    Publication statusPublished - 2003 Sep

    Keywords

    • A priori estimates
    • Cross-diffusion
    • Global existence
    • Self-diffusion

    ASJC Scopus subject areas

    • Mathematics(all)
    • Analysis
    • Applied Mathematics
    • Discrete Mathematics and Combinatorics

    Fingerprint Dive into the research topics of 'Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with weak cross-diffusion'. Together they form a unique fingerprint.

  • Cite this