华东师范大学学报（自然科学版） >

2021 , Vol. 2021 >Issue 1: 16 - 27

DOI: https://doi.org/10.3969/j.issn.1000-5641.201911046

数学

带有衰退记忆的非自治经典反应扩散方程在非线性边界下解的渐近性

  • 梁玉婷 ,
  • 汪璇
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  • 西北师范大学 数学与统计学院, 兰州　730070

收稿日期: 2019-11-25

  网络出版日期: 2021-01-28

基金资助

国家自然科学基金(11761062, 11561064, 11661071)

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Asymptotic behavior of solutions for the non-autonomous classical reaction-diffusion equation with nonlinear boundary conditions and fading memory

  • Yuting LIANG ,
  • Xuan WANG
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  • College of Mathematics and Statistics, Northwest Normal University, Lanzhou　730070, China

Received date: 2019-11-25

  Online published: 2021-01-28

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摘要

本文研究了带有衰退记忆的非自治经典反应扩散方程解的长时间动力学行为, 当内部非线性项和边界非线性项均以任意阶多项式增长并满足一定的平衡条件, 且外力项仅为平移有界而非平移紧时, 运用收缩函数方法和过程理论, 证明了一致吸引子在 $L^{2}(\Omega)\times L_\mu^2(\mathbb R^+; H_{0}^1(\Omega))$ 中的存在性及其吸引子的拓扑结构. 该结果改进和推广了一些已有的结果.

关键词： 非自治经典反应扩散方程; 一致吸引子; 非线性边界; 衰退记忆; 任意阶多项式增长

本文引用格式

梁玉婷 , 汪璇 . 带有衰退记忆的非自治经典反应扩散方程在非线性边界下解的渐近性[J]. 华东师范大学学报（自然科学版）, 2021 , 2021(1) : 16 -27 . DOI: 10.3969/j.issn.1000-5641.201911046

Abstract

In this paper, we study the long-time dynamic behavior of solutions for the non-autonomous classical reaction-diffusion equation with nonlinear boundary conditions and fading memory, where the internal nonlinearity and boundary nonlinearity adheres to polynomial growth of arbitrary order as well as the balance condition. In addition, the forcing term is translation bounded, rather than translation compact, by use of contractive function method and process theory. The existence and the topological structure of uniform attractors in $L^{2}(\Omega)\times L_\mu^2(\mathbb R^+; H_{0}^1(\Omega))$ are proven. This result extends and improves existing research in the literature.

Key words： non-autonomous classical reaction-diffusion equation; uniform attractors; nonlinear boundary; fading memory; polynomial growth of arbitrary order

参考文献

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