具有衰退记忆的非自治非经典扩散方程的强吸引子

Strong Attractors for the Non-autonomous Nonclassical Diffusion Equations with Fading Memory

在强拓扑空间H_0~1(Ω)∩H^2(Ω)×L_μ~2(R^+;H_0~1(Ω)∩H^2(Ω))中,讨论了具有衰退记忆的非自治非经典扩散方程当非线性项临界增长时的长时间动力学行为.当与时间相关的外力项仅满足平移有界而非平移紧时,首先得到了强解的渐近正则性,然后获得了强吸引子的存在性及其结构与正则性.该结果推广和改进了一些已有结果.

The authors discuss the long-time dynamical behavior of the non-autonomous nonclassical diffusion equation with fading memory in the strong topological space H01 （Ω） N H2 （Ω）× L2u （R＋; H0^1 （Ω） N H2 （Ω）） when nonlinearity is critical. At first the asymptotic regu- larity of strong solutions is obtained, and then the existence of a compact uniform attractor together with its structure and regularity is obtained, while the time-dependent forcing term is only translation bounded instead of translation compact. The result extends and improves some known results.