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带有衰退记忆的非自治经典反应扩散方程在非线性边界下解的渐近性

梁玉婷 汪璇

梁玉婷, 汪璇. 带有衰退记忆的非自治经典反应扩散方程在非线性边界下解的渐近性[J]. 华东师范大学学报(自然科学版), 2021, (1): 16-27. doi: 10.3969/j.issn.1000-5641.201911046
引用本文: 梁玉婷, 汪璇. 带有衰退记忆的非自治经典反应扩散方程在非线性边界下解的渐近性[J]. 华东师范大学学报(自然科学版), 2021, (1): 16-27. doi: 10.3969/j.issn.1000-5641.201911046
LIANG Yuting, WANG Xuan. Asymptotic behavior of solutions for the non-autonomous classical reaction-diffusion equation with nonlinear boundary conditions and fading memory[J]. Journal of East China Normal University (Natural Sciences), 2021, (1): 16-27. doi: 10.3969/j.issn.1000-5641.201911046
Citation: LIANG Yuting, WANG Xuan. Asymptotic behavior of solutions for the non-autonomous classical reaction-diffusion equation with nonlinear boundary conditions and fading memory[J]. Journal of East China Normal University (Natural Sciences), 2021, (1): 16-27. doi: 10.3969/j.issn.1000-5641.201911046

带有衰退记忆的非自治经典反应扩散方程在非线性边界下解的渐近性

doi: 10.3969/j.issn.1000-5641.201911046
基金项目: 国家自然科学基金(11761062, 11561064, 11661071)
详细信息
    通讯作者:

    汪 璇, 女, 博士, 教授, 研究方向为非线性微分方程和无穷维动力系统. E-mail: wangxuan@nwnu.edu.cn

  • 中图分类号: O175.29

Asymptotic behavior of solutions for the non-autonomous classical reaction-diffusion equation with nonlinear boundary conditions and fading memory

  • 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.
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出版历程
  • 收稿日期:  2019-11-25
  • 刊出日期:  2021-01-27

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