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

Autor:	Gleiciane S. Aragão, Flank D. M. Bezerra
Rok vydání:	2020
Předmět:	Mathematics::Dynamical Systems Dynamical systems theory Mathematics::Category Theory Applied Mathematics Mathematical analysis Pullback attractor Damped wave Wave equation Analysis Mathematics
Zdroj:	Topological Methods in Nonlinear Analysis. :1-27
ISSN:	1230-3429
DOI:	10.12775/tmna.2019.118
Popis:	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 $\varepsilon=0$.
Databáze:	OpenAIRE
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