LOWER SEMICONTINUITY OF THE PULLBACK ATTRACTORS OF NON-AUTONOMOUS DAMPED WAVE EQUATIONS WITH TERMS CONCENTRATING ON THE BOUNDARY

Author(s)

Bezerra, Flank D. M. ^[1] ; Aragao, Gleiciane S. ^[2]

Affiliation

^[1] Univ Fed Paraiba, Dept Matemat, Cidade Univ, Campus 1, BR-58051900 Joao Pessoa, Paraiba - Brazil

^[2] Univ Fed Sao Paulo, Dept Ciencias Exatas & Terra, Av Conceicao 515, BR-09920000 Diadema, SP - Brazil

• Document type: Journal article
• Source: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS; v. 57, n. 1, p. 173-199, MAR 2021.
• Web of Science Citations: 0

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 epsilon 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 epsilon = 0. Finally, we obtain the continuity of the pullback attractors at epsilon = 0. (AU)

• FAPESP's process: 19/04476-6 - Dynamic systems in infinite dimensional spaces
• Grantee: Gleiciane da Silva Aragão
• Support Opportunities: Regular Research Grants