AIMS Mathematics (Oct 2021)

The existence of a compact global attractor for a class of competition model

  • Yanxia Wu

DOI
https://doi.org/10.3934/math.2021014
Journal volume & issue
Vol. 6, no. 1
pp. 210 – 222

Abstract

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This paper is concerned with the existence of a compact global attractor for a class of competition model in n−dimensional (n ≥ 1) domains. Using mathematical induction and more detailed interpolation estimates, especially Gagliardo-Nirenberg inequality, we obtain the existence of a compact global attractor, which implies the uniform boundedness of the global solutions. In particular, we get that the Shigesada-Kawasaki-Teramoto competition model has a compact global attractor for n < 10. The result of the S-K-T model extends the existence results of compact global attractor in [21] from n < 8 to n < 10, and extends the uniform boundedness results of the global solutions in [17] to the non-convex domain.

Keywords