Acta mathematica scientia,Series A ›› 2023, Vol. 43 ›› Issue (1): 82-92.

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

Zhu Kaixuan1,*(),Sun Tao1(),Xie Yongqin2()   

  1. 1College of Mathematics and Physics Science, Hunan University of Arts and Science, Hunan Changde 415000
    2School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114
  • Received:2021-10-12 Revised:2022-08-05 Online:2023-02-26 Published:2023-03-07
  • Supported by:
    Hunan Province Natural Science Foundation of China(2022JJ30417);Scientific Research Fund of Hunan Provincial Education Department(21A0414);Scientific Research Fund of Hunan Provincial Education Department(21B0617);Hunan University of Arts and Science(STIT): Numerical Calculation & Stochastic Process with Their Applications


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