Asymptotic behavior of solutions for the non-autonomous classical reaction-diffusion equation with nonlinear boundary conditions and fading memory
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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
$L^{2}(\Omega)\times L_\mu^2(\mathbb R^+; H_{0}^1(\Omega))$ 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.-
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
Abstract: 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$L^{2}(\Omega)\times L_\mu^2(\mathbb R^+; H_{0}^1(\Omega))$ are proven. This result extends and improves existing research in the literature. -
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