Dynamics of wave equations with moving boundary

作者：Ma To Fu^*; Marin Rubio Pedro; Surco Chuno Christian Manuel

来源：Journal of Differential Equations, 2017, 262(5): 3317-3342.

DOI：10.1016/j.jde.2016.11.030

• Wave equation
• Non-cylindrical domain
• Non-autonomous system
• Pullback attractor
• Critical exponent

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.

• 出版日期2017-3-5