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  

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

作　　者：梁玉婷 汪璇 LIANG Yuting;WANG Xuan(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《华东师范大学学报（自然科学版）》2021年第1期16-27,共12页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金(11761062,11561064,11661071)。

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L2(Ω)×Lμ2(R+;H01(Ω))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.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 L2(Ω) × Lμ2(R+;H01(Ω)) are proven. This result extends and improves existing research in the literature.

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 

分 类 号：O175.29[理学—数学]