衰退记忆型经典反应扩散方程在非线性边界条件下解的渐近性

doi:10.3969/j.issn.1000-5641.2019.03.003

华东师范大学学报(自然科学版) ›› 2019, Vol. 2019 ›› Issue (3): 13-23.doi: 10.3969/j.issn.1000-5641.2019.03.003

衰退记忆型经典反应扩散方程在非线性边界条件下解的渐近性

汪璇, 赵涛, 张玉宝

西北师范大学数学与统计学院, 兰州 730070

收稿日期:2018-04-02 出版日期:2019-05-25 发布日期:2019-05-30
作者简介:汪璇,女,博士,教授,研究方向为非线性微分方程和无穷维动力系统理论应用.E-mail:wangxuan@nwnu.edu.cn.
基金资助:
国家自然科学基金（11761062，11561064，11661071）；西北师范大学青年教师科研能力提升计划（NWNU-LKQN-14-6）

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

WANG Xuan, ZHAO Tao, ZHANG Yu-bao

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received:2018-04-02 Online:2019-05-25 Published:2019-05-30

摘要/Abstract

摘要： 本文研究了记忆型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超临界指数增长并满足一定的平衡条件时，运用抽象函数理论和半群理论，证明了该方程的全局吸引子在L²（Ω）×L_μ²（R⁺；H¹（Ω））中的存在性，此结果改进和推广了一些已有的结果.

关键词: 经典反应扩散方程, 非线性边界, 衰退记忆, 任意阶多项式增长

Abstract: In this paper, we study the asymptotic behavior of solutions for the classical reaction-diffusion equation with memory. Through the use of abstract function theory and semigroup theory, the existence of a global attractor in L²(Ω)×L_μ²(R⁺; H¹(Ω)) is proven when the internal nonlinearity and boundary nonlinearity adhere to polynomial growth of arbitrary order as well as the balance condition. This result extends and improves some known results.

Key words: classical reaction-diffusion equation, nonlinear boundary, fading memory, polynomial growth of arbitrary order

中图分类号:

O175.29

汪璇, 赵涛, 张玉宝. 衰退记忆型经典反应扩散方程在非线性边界条件下解的渐近性[J]. 华东师范大学学报(自然科学版), 2019, 2019(3): 13-23.

WANG Xuan, ZHAO Tao, ZHANG Yu-bao. Asymptotic behavior of solutions for the classical reaction-diffusion equation with nonlinear boundary conditions and fading memory[J]. Journal of East China Normal University(Natural Sc, 2019, 2019(3): 13-23.

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衰退记忆型经典反应扩散方程在非线性边界条件下解的渐近性

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

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