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.

中文翻译：

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一类竞争模型的紧凑型全球吸引子的存在

本文关注的是一个紧凑的全局吸引子的存在，在一类竞争模型的ñ维（ñ ≥1）域。使用数学归纳法和更详细的插值估计，尤其是Gagliardo-Nirenberg不等式，我们获得了紧凑的全局吸引子的存在，这暗示了全局解的一致有界性。特别是，我们得到了Shigesada-Kawasaki-Teramoto竞争模型具有n <10的紧凑全局吸引子。SKT模型的结果将[21]中的紧凑型全局吸引子的存在结果从n <8扩展到n <10 ，并将[17]中全局解的一致有界结果扩展到非凸域。