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 $\varepsilon$ 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 $\varepsilon=0$. Finally, we obtain the continuity of the pullback attractors at $\varepsilon=0$.
"Lower semicontinuity of the pullback attractors of non-autonomous damped wave equations with terms concentrating on the boundary." Topol. Methods Nonlinear Anal. 57 (1) 173 - 199, 2021. https://doi.org/10.12775/TMNA.2019.118