带衰退记忆的非自治非经典扩散方程的吸引子  

Attractors for the non-autonomous nonclassical diffusion equation with fading memory

作　　者：李有玲 汪璇 LI You-ling;WANG Xuan(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《山东大学学报（理学版）》2021年第9期66-80,共15页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11761062,11961059,12061062)。

摘　　要：在空间H^(1)_(0)(Ω)×L^(2)_(μ)(R^(+);H^(1)_(0)(Ω))中,当非线性项f(u,t)次临界增长时,讨论了具有衰退记忆的非自治非经典扩散方程解的长时间动力学行为。当外力项仅满足平移有界而非平移紧时,通过渐近正则估计技术,得到了紧一致吸引子的存在性及其拓扑结构。The long-time dynamical behavior of solutions for the non-autonomous nonclassical diffusion equation with fading memory and subcritical nonlinearity is discussed in the space H^(1)_(0)(Ω)×L^(2)_(μ)(R^(+);H^(1)_(0)(Ω)).When the external term g(x,t)is only translation bounded instead of translation compact,by means of the asymptotic regularity estimate technique,the existence and topological structure of a compact uniform attractor is obtained.

关 键 词：非自治非经典扩散方程 一致吸引子 次临界增长 渐近正则性 衰退记忆 

分 类 号：O175.26[理学—数学] O175.29[理学—基础数学]