带时间依赖记忆核和非局部扩散的热传导方程解的长时间行为
Long-Term Behavior of Heat Conduction Equation Solutions with Time-Dependent Memory and Non-Local Diffusion
DOI: 10.12677/AAM.2023.1212517, PDF, 下载: 109  浏览: 2,831  国家自然科学基金支持
作者: 黄晶朋, 汪 璇*：西北师范大学，数学与统计学院，甘肃 兰州
关键词: 非局部反应扩散方程；时间依赖记忆核；适定性；时间依赖全局吸引子；存在性；Non-Local Reaction Diffusion Equation； Time-Dependent Memory Kernel； Well-Posed-Ness； Time-Dependent Global Attractors； Existence
摘要: 本文分析了带时间依赖记忆核和非局部扩散的热传导方程解的长时间行为。 当非线性项满足次临界增长条件时，在时间依赖空间中，首先利用 Galerkin 逼近法得到了解的适定性和正则性，进而利用分解技巧和积分估计法证明了时间依赖全局吸引子的存在性。
Abstract: In this paper,we analysize the long-time behavior of solutions for the non-local diffu- sion equation with time-dependent memory kernel. When nonlinear term adheres to subcritical growth condition and in the time-dependent space by use of the Galerkin approximation method, the well-posedness and the regularity of the solution arise achieved. And then the existence of the time-dependent global attractors is proved by applying the delicate integral estimation method and decom- position technique.
文章引用：黄晶朋, 汪璇. 带时间依赖记忆核和非局部扩散的热传导方程解的长时间行为[J]. 应用数学进展, 2023, 12(12): 5267-5291. https://doi.org/10.12677/AAM.2023.1212517

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