具有时间依赖记忆核的粘弹性方程的吸引子

doi:10.12677/PM.2022.127122

期刊菜单

具有时间依赖记忆核的粘弹性方程的吸引子
Attractors for the Viscoelastic Equationwith Time-Dependent Memory Kernel

DOI: 10.12677/PM.2022.127122, PDF, HTML, 国家自然科学基金支持
作者: 袁海燕, 汪璇^*：西北师范大学数学与统计学院，甘肃兰州
关键词: 粘弹性方程；时间依赖记忆核；时间依赖全局吸引子；Viscoelastic Equation； Time-Dependent Memory Kernel； Time-Dependent Global Attractors

摘要: 对于具有时间依赖记忆核的粘弹性方程，本文研究了该方程解的长时间动力学行为。当非线性项 f 的增长指数 p 满足1≤p≤5时，在新的理论框架下，利用积分估计方法得到了解的适定性。同时，当 p 满足1≤p<5时，证明了时间依赖全局吸引子的存在性以及不变性。

Abstract: In this paper, we investigate the long-time dynamical behavior of solutions for the viscoelastic equation with time-dependent memory kernel. When the growth exponent p of nonlinearity f(u) is up to 1≤p≤5, the well-posedness of the solutions is proved by using the integral estimation method, and we obtained an invariant time-dependent global attractor when 1≤p<5 .

文章引用：袁海燕, 汪璇. 具有时间依赖记忆核的粘弹性方程的吸引子[J]. 理论数学, 2022, 12(7): 1103-1124. https://doi.org/10.12677/PM.2022.127122

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