带有分布导数的反应扩散方程在$\Bbb R ^{n}$中全局吸引子的存在性

Abstract

Abstract:

In this paper, we consider the long-time behavior of solutions for a class of reaction-diffusion equations in $\Bbb R ^{n}$ with weighted terms $V(x)$ and some distribution derivatives in inhomogeneous terms. We prove that the $\big(L^{2}(\Bbb R ^{n}), L^{2}(\Bbb R ^{n})\cap L^{p}(\Bbb R ^{n})\big)$-global attractors indeed can attract every bounded subset of $L^{2}(\Bbb R ^{n})$ with the $L^{2}\cap L^{p+\delta_{1}}$-norm for any $\delta_{1}\in [0,+\infty)$.

Key words: Reaction-diffusion equations, Asymptotic higher-order integrability, Global attractors

CLC Number:

O193

Zhu Kaixuan, Sun Tao, Xie Yongqin. Global Attractors for a Class of Reaction-Diffusion Equations with Distribution Derivatives in $\Bbb R ^{n}$[J].Acta mathematica scientia,Series A, 2023, 43(1): 82-92.

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Global Attractors for a Class of Reaction-Diffusion Equations with Distribution Derivatives in $\Bbb R ^{n}$

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