衰退记忆型经典反应扩散方程在非线性边界条件下解的渐近性

汪璇; 赵涛; 张玉宝

doi:10.3969/j.issn.1000-5641.2019.03.003

衰退记忆型经典反应扩散方程在非线性边界条件下解的渐近性

doi: 10.3969/j.issn.1000-5641.2019.03.003

西北师范大学数学与统计学院, 兰州 730070

基金项目:

国家自然科学基金 11761062

国家自然科学基金 11561064

国家自然科学基金 11661071

西北师范大学青年教师科研能力提升计划 NWNU-LKQN-14-6

详细信息

作者简介:
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理论应用.E-mail:wangxuan@nwnu.edu.cn

中图分类号: O175.29
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- 文章访问数: 140
- HTML全文浏览量: 62
- PDF下载量: 87
- 被引次数: 0
出版历程
- 收稿日期: 2018-04-02
- 刊出日期: 2019-05-25

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

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

摘要

摘要: 本文研究了记忆型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超临界指数增长并满足一定的平衡条件时，运用抽象函数理论和半群理论，证明了该方程的全局吸引子在${L^2}\left( \Omega \right) \times L_\mu ^2\left( {{\mathbb{R}^ + };{H^1}\left( \Omega \right)} \right)$中的存在性，此结果改进和推广了一些已有的结果.
- 经典反应扩散方程 /
- 非线性边界 /
- 衰退记忆 /
- 任意阶多项式增长
Abstract: In this paper, we study the asymptotic behavior of solutions for the classical reaction-diffusion equation with memory. Through the use of abstract function theory and semigroup theory, the existence of a global attractor in ${L^2}\left( \Omega \right) \times L_\mu ^2\left( {{\mathbb{R}^ + };{H^1}\left( \Omega \right)} \right)$ is proven when the internal nonlinearity and boundary nonlinearity adhere to polynomial growth of arbitrary order as well as the balance condition. This result extends and improves some known results.
- classical reaction-diffusion equation /
- nonlinear boundary /
- fading memory /
- polynomial growth of arbitrary order

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参考文献(16)

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