Regularity of Invariant Sets in Variable Internal Damped Wave Equations

• 作者: Gao-cheng YUE Yu-xin LIANG Jia-jia YANG
• 来源期刊: 应用数学学报（英文版）
• 年，卷（期）: 2020,（4）
• 页码范围: 952-974
• 页数: 23页
• 语种: 英文

摘要

In this paper we prove that every compact invariant subset A associated with the semigroup{Sn,k(t)}t≥0 generated by wave equations with variable damping,either in the interior or on the boundary of the domain Ω,where Ω ? R3 is a smooth bounded domain,in H01(Ω)×L2(Ω)is in fact bounded in D(Bo)×H10(Ω).As an application of our results,we obtain the upper-semicontinuity for global attractor of the weakly damped semilinear wave equation in the norm of H1(Ω)×L2(Ω)when the interior variable damping converges to the boundary damping in the sense of distributions.