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

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 a...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 1; pp. 210 - 222
Main Author Wu, Yanxia
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
global attractor
global existence
mpetition model
uniform boundedness
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021014