带有某种遗传特征的非经典反应扩散方程的渐近行为

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带有某种遗传特征的非经典反应扩散方程的渐近行为朱凯旋¹, 谢永钦², 张江卫²1. 洞庭湖生态经济区建设与发展湖南省协调创新中心 & 湖南文理学院数理学院常德 415000;
2. 长沙理工大学数学与统计学院长沙 410114 Asymptotic Behavior of the Nonclassical Reaction-diffusion Equations Containing some Hereditary Characteristic Kai Xuan ZHU¹, Yong Qin XIE², Jiang Wei ZHANG²1. Hunan Province Cooperative Innovation Center for the Construction and Development of Dongting Lake Ecological Economic Zone, College of Mathematics and Physics Science, Hunan University of Arts and Science, Changde 415000, P. R. China;
2. School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, P. R. China

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摘要本文证明带有时滞项g（t，u_t）的非经典反应扩散方程在依赖于时间的空间中拉回吸引子的存在性，其中外力项k（x）∈H^-1（Ω），非线性项f分别满足临界指数增长和任意q-1（q≥2）次多项式增长.

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收稿日期: 2020-02-13

MR (2010):

O193

基金资助:湖南省自然科学基金（2018JJ2416）及湖南省教育厅科学研究基金（20C1263）；湖南文理学院科技创新团队资助项目（数值计算与随机过程及其应用）

通讯作者:朱凯旋,E-mail:zhukx12@163.comE-mail: zhukx12@163.com

作者简介: 谢永钦,E-mail:xieyq@csust.edu.cn;张江卫,E-mail:zjwmath@163.com

引用本文:

朱凯旋, 谢永钦, 张江卫. 带有某种遗传特征的非经典反应扩散方程的渐近行为[J]. 数学学报, 2021, 64(5): 721-736. Kai Xuan ZHU, Yong Qin XIE, Jiang Wei ZHANG. Asymptotic Behavior of the Nonclassical Reaction-diffusion Equations Containing some Hereditary Characteristic. Acta Mathematica Sinica, Chinese Series, 2021, 64(5): 721-736.

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