摘要
当任意阶多项式增长的非线性项为耗散,且外力项仅属于L^2(Ω)时,研究了带衰退记忆的经典反应扩散方程的解在强拓扑空间H_0~1(Ω)×L_μ~2(R^+;D(A))的长时间行为.应用抽象函数理论、半群理论以及新的估计技巧,在拓扑空间H_0~1(Ω)×L_μ~2(R^+;D(A))上,验证了强解半群的渐近紧性并且证明了强全局吸引子的存在性.
This paper deals with the long-time behavior of solutions for the classical re- action diffusion equations with fading memory in the strong topological space H0^1（Ω）×Lμ^2（R^＋;D（A））, where the nonlinearity with polynomial growth of arbitrary order is dissipative, and the forcing term only belongs to L2（Ω）. Applying the abstract function theory, the semigroup theory and some new estimate techniques, the authors prove the asymptotic compactness of solutions and obtain the existence of global attractor in the strong topological space H0^1（Ω）×Lμ^2（R^＋;D（A））.
出处
《数学年刊（A辑）》
CSCD
北大核心
2015年第3期265-276,共12页
Chinese Annals of Mathematics
基金
甘肃省自然科学基金(No.145RJZA112)
国家自然科学基金(No.11361053,No.11201204,No.11261053)的资助
关键词
经典反应扩散方程
强全局吸引子
任意阶多项式增长
衰退记忆
Classical reaction diffusion equations, Strong global attractor,Polynomial growth of arbitrary order, Fading memory
