Dynamics of wave equations with moving boundary

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:262

Article

Ma, To Fu¹  Marin-Rubio, Pedro²  Surco Chuno, Christian Manuel³ 

[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13566590 Sao Carlos, SP, Brazil

[2] Univ Seville, Dept Ecuac Diferenciales & Anal Numer, Apdo Correos 1160, E-41080 Seville, Spain

[3] Univ Fed Tecnol Parana, Campus Curitiba, BR-80230901 Curitiba, PR, Brazil

关键词: Wave equation;    Non-cylindrical domain;    Non-autonomous system;    Pullback attractor;    Critical exponent;   

DOI  :  10.1016/j.jde.2016.11.030

来源: Elsevier

【 摘 要 】

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, tau) : X-tau -> X-t, where X-t 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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free