具临界指数的强阻尼波方程依赖时间全局吸引子

Time-dependent global attractors for strongly damped wave equation with critical exponent

摘要:

本文考虑具有临界增长指数的强阻尼波方程解的长时间行为,得到了过程的耗散性, 利用过程分解技巧得到了过程的渐近紧性, 最后给出了方程依赖时间吸引子的存在性.

Abstract:

In this paper, we are concerned with the longtime behavior of the non-autonomous strongly damped wave equations. We first obtain the dissipativity of the process associated with the equations. Then, by using the skill of the operator decomposition, we prove the asymptotic compactness of the process. Finally, we give out the existence of the time-dependent attractors for the equation.