Dynamics of wave equations with moving boundary

详细信息    查看全文

• 作者：To Fu Ma^a ; ^{matofu@icmc.usp.br} ; Pedro Marí ; n-Rubio^b ; ^pmr@us.es ; Christian Manuel Surco Chuñ ; o^c ; ^{christianchuno@utfpr.edu.br}
• 关键词：35R37 ; 35L70 ; 35B41
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 March 2017
• 年：2017
• 卷：262
• 期：5
• 页码：3317-3342
• 全文大小：371 K
• 卷排序：262

文摘

This paper is concerned with long-time dynamics of weakly damped semilinear wave equations defined on domains with moving boundary. Since the boundary is a function of the time variable the problem is intrinsically non-autonomous. Under the hypothesis that the lateral boundary is time-like, the solution operator of the problem generates an evolution process U(t,τ):Xτ→XtU(t,τ):Xτ→Xt, where XtXt are time-dependent Sobolev spaces. Then, by assuming the domains are expanding, we establish the existence of minimal pullback attractors with respect to a universe of tempered sets defined by the forcing terms. Our assumptions allow nonlinear perturbations with critical growth and unbounded time-dependent external forces.