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

Yanxia Wu; Yanxia Wu

doi:10.3934/math.2021014

AIMS Mathematics

2021, Volume 6, Issue 1: 210-222. doi: 10.3934/math.2021014

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Research article

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

Yanxia Wu ^,

School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, P. R. China

Received: 10 July 2020 Accepted: 24 September 2020 Published: 09 October 2020
MSC : 35A01, 35B41, 35K57, 92D40

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.
- competition model,
- global existence,
- global attractor,
- uniform boundedness
Citation: Yanxia Wu. The existence of a compact global attractor for a class of competition model[J]. AIMS Mathematics, 2021, 6(1): 210-222. doi: 10.3934/math.2021014

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Abstract

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.

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