Pullback attractor for a dynamic boundary non-autonomous problem with Infinite delay

In this work we prove the existence of solution for a p-Laplacian non-autonomous problem with dynamic boundary and infinite delay. We ensure the existence of pullback attractor for the multivalued process associated to the non-autonomous problem we are concerned. Finally, we also prove the existence of a more general attractor for the problem known as D-pullback attractor.Conselho Nacional de Desenvolvimento Científico e TecnológicoMinisterio de Economía y CompetitividadFondo Europeo de Desarrollo RegionalJunta de Andalucí

Dynamics of wave equations with moving boundary

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 → Xt, where Xt are timedependent 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.Conselho Nacional de Desenvolvimento Científico e TecnológicoMinisterio de EducaciónMinisterio de Ciencia e Innovació