具临界指数的强阻尼波方程的时间依赖全局吸引子（英文）

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

本文考虑如下具有临界增长指数的强阻尼波方程ε(t)u_(tt)-Δu_t-Δu+φ(u)=f解的长时间行为.本文首先得到过程的耗散性,然后利用过程分解技巧得到过程的渐近紧性,最后给出了方程依赖于时间的吸引子的存在性.

In this paper,we are concerned with the longtime behavior of the non-autonomous strongly damped wave equation ε（t） u tt -Δ u t -Δ u＋φ（u）=f. We first obtain the dissipativity of the process associated with the equation.Then, by using the skill of operator decomposition,we prove the asymptotic compactness of the process.Finally,we prove the existence of the time-dependent attractors for the equation.