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 Fading Memory

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.

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（Ω）. 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 L2（Ω）×Lμ2（R＋;H01（Ω））. The result extends and improves some results by Chepyzhov et al. （2006） and Zhong et al. （2006）.