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2021 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
Topol. Methods Nonlinear Anal. 57(1): 173-199 (2021). DOI: 10.12775/TMNA.2019.118

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 $\varepsilon=0$.

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Flank D. M. Bezerra. Gleiciane S. Aragão. "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

Information

Published: 2021
First available in Project Euclid: 10 September 2020

Digital Object Identifier: 10.12775/TMNA.2019.118

Rights: Copyright © 2020 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.57 • No. 1 • 2021
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