| 汪璇,张玉宝,杨璐.带有衰退记忆的非自治经典反应扩散方程的吸引子[J].数学年刊A辑,2019,(1):079~92 |
| 带有衰退记忆的非自治经典反应扩散方程的吸引子 |
| Attractor for the Non-autonomous Classical Reaction Diffusion Equations with Fading Memory |
| Received:September 30, 2016 Revised:June 06, 2018 |
| DOI：10.16205/j.cnki.cama.2019.0007 |
| 中文关键词: Non-autonomous classical reaction diffusion equation, Uniform linebreakattractor, Polynomial growth of arbitrary order, Fading memory |
| 英文关键词:Non-autonomous classical reaction diffusion equation, Uniform linebreakattractor, Polynomial growth of arbitrary order, Fading memory |
| 基金项目: |
| Author Name | Affiliation | E-mail | | WANG Xuan | College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, China. | wangxuan@nwnu.edu.cn | | ZHANG Yubao | College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, China. | blcx07@qq.com | | YANG Lu | School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, China. | yanglu@lzu.edu.cn |
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| 中文摘要: |
| 当非线性项以任意阶多项式增长, 且外力项仅为平移有界而非平移紧时,
研究了非自治经典反应扩散方程解的长时间动力学行为. 应用抽象函数理论和新的估计技术,
在拓扑空间$L^2(\Omega)\times L_\mu^2(\mathbb R^+; H_0^1(\Omega))$上,
证明了一致吸引子的存在性. 该结果改进和推广了Chepyzhov 等
(2006)和钟承奎等(2006)的相应结果. |
| 英文摘要: |
| The long-time dynamical behavior of the non-autonomous classical
reaction diffusion equations with fading memory is studied, when the
nonlinearity adheres to polynomial growth of arbitrary order and the
forcing term is only translation bounded instead of translation compact. By virtue of the
contract function theory and some new estimate
technique, the author prove the existence of uniform attractors in the space
$L^2(\Omega)\times L_\mu^2(\mathbb R^+; H_0^1(\Omega))$. The result
extends and improves some results by Chepyzhov et al. (2006) and Zhong et al. (2006). |
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