Lower semicontinuity of the pullback attractors of non-autonomous damped wave equations with terms concentrating on the boundary - Bezerra, Flank D. M.; Aragão, Gleiciane S. (Topological Methods in Nonlinear Analysis, 2020)
In this paper we analyze the asymptotic behavior of the pullback attractors for non-autonomous dynamical systems generated by a family of non-autonomous damped wave equations when some reaction terms are concentrated in a neighbourhood of the boundary and this neighbourhood shrinks to boundary as a parameter ε goes to zero. We show the gradient-like structure of the limit pullback attractor, the existence and continuity of global hyperbolic solutions and the lower semicontinuity of the pullback attractors at ε=0. Finally, we obtain the continuity of the pullback attractors at ε=0.