Lower semicontinuity of the pullback attractors of non-autonomous damped wave equations with terms concentrating on the boundary
DOI:
https://doi.org/10.12775/TMNA.2019.118Keywords
Wave equation, non-autonomous, concentrating terms, pullback attractor, gradient-like, hyperbolic solution, lower semicontinuityAbstract
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 $\varepsilon=0$.References
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