| 汪璇,朱宗伟,马巧珍.带衰退记忆的经典反应扩散方程的全局吸引子[J].数学年刊A辑,2014,35(4):423~434 |
| 带衰退记忆的经典反应扩散方程的全局吸引子 |
| Global Attractors for the Classical Reaction Diffusion Equations with FadingMemory |
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| DOI： |
| 中文关键词: 经典反应扩散方程, 全局吸引子, 任意阶多项式增长, 衰退记忆 |
| 英文关键词:Classical reaction diffusion equations, Global
attractors, Polynomial growth of arbitrary order, Fading memory |
| 基金项目:国家自然科学基金 (No.11361053, No.11101404, No.,11201204, No.11101134, No.11261053) 和西北师范大学青年教师科研能力提升计划项目 (No.NWNU-LKQN-11-5) |
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| 中文摘要: |
| 当非线性项满足任意阶多项式增长且外力项仅属于$H^{-1}(\Omega)$时,
研究了带衰退记忆的经典反应扩散方程的长时间动力学行为. 应用抽象函数理论、半群理论以及
新的估计技巧, 在空间$L^2(\Omega)\times L_\mu^2(\mathbb R^+; H_0^1(\Omega))$上证明了全局吸引子的存在性.
该结果改进和推广了 Chepyzhov 等人 (2006) 及 Zhong 等人 (2006) 的相应结果. |
| 英文摘要: |
| The authors study the long-time dynamical behavior of the classical
reaction diffusion equations with fading memory, when the
nonlinearity adheres to polynomial growth of arbitrary order and the
forcing term belongs only to $H^{-1}(\Omega)$. By virtue of the
contract function theory, semigroup theory and some new estimate
technique, the authors prove the existence of global 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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