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带衰退记忆的经典反应扩散方程的全局吸引子
引用本文: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(中文版),2014,35(4):423-434.
作者姓名:汪璇  朱宗伟  马巧珍
作者单位:西北师范大学数学与统计学院, 兰州 730070.;西北师范大学数学与统计学院, 兰州 730070.;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 (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)
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)(Ω)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(Ω)×L_μ~2(R~+;H_0~1(Ω))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.

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

Global Attractors for the Classical Reaction Diffusion Equations with Fading Memory
WANG Xuan,ZHU Zongwei and MA Qiaozhen.Global Attractors for the Classical Reaction Diffusion Equations with Fading Memory[J].Chinese Annals of Mathematics,2014,35(4):423-434.
Authors:WANG Xuan  ZHU Zongwei and MA Qiaozhen
Institution:Northwest Normal University, Lanzhou 730070, China.;Northwest Normal University, Lanzhou 730071, China.;Northwest Normal University, Lanzhou 730072, China.
Abstract: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).
Keywords:Classical reaction diffusion equations  Global attractors  Polynomial growth of arbitrary order  Fading memory
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