Lower semicontinuity of the pullback attractors of non-autonomous damped wave equations with terms concentrating on the boundary

Flank D. M. Bezerra, Gleiciane S. Aragão

Abstract


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 $\varepsilon=0$.

Keywords


Wave equation; non-autonomous; concentrating terms; pullback attractor; gradient-like; hyperbolic solution; lower semicontinuity

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References


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