时间依赖记忆型经典反应扩散方程的吸引子
Attractors for the Classical Reaction Diffusion Equation with Time-DependentMemory Kernel
DOI: 10.12677/PM.2023.135150, PDF, HTML, 下载: 115  浏览: 211  国家自然科学基金支持
作者: 李玉娜, 汪 璇：西北师范大学，数学与统计学院，甘肃 兰州
关键词: 经典反应扩散方程；时间依赖记忆核；适定性；时间依赖全局吸引子；存在性；Classical Reaction Diffusion Equation； Quad Time-Dependent Memory Kernel； Well-Posed-Ness； Time-Dependent Global Attractors； Existence
摘要: 本文考虑了具有时间依赖记忆核的经典反应扩散方程，当非线性项满足次临界增长时，在时间依赖空间中方程解的长时间动力学行为。在新的理论框架下，利用积分估计方法以及分解技术得到了解的适定性和正则性，进而证明了时间依赖全局吸引子的存在性。
Abstract: In this paper, we consider the long-time dynamical behavior of solutions for the classical reaction diffusion equation with time-dependent memory kernel when nonlinear term adheres to subcritical growth in the time-dependent space . Under the new theorical framework, the well-posedness and the regularity of the solution, the existence of the time-dependent global attractors are proved by using the delicate integral estimation method and decomposition technique.
文章引用：李玉娜, 汪璇. 时间依赖记忆型经典反应扩散方程的吸引子[J]. 理论数学, 2023, 13(5): 1456-1482. https://doi.org/10.12677/PM.2023.135150

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