Continuity of pullback attractors for evolution processes associated with semilinear damped wave equations with time-dependent coefficients

Author(s)

Aragao, Gleiciane S. ^[1] ; Bezerra, Flank D. M. ^[2] ; Figueroa-Lopez, Rodiak N. ^[3] ; Nascimento, Marcelo J. D. ^[3]

Affiliation

^[1] Univ Fed Sao Paulo, Dept Ciencias Exatas & Terra, Av Conceicao, 515, Ctr, BR-09920000 Diadema, SP - Brazil

^[2] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba - Brazil

^[3] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: Journal of Differential Equations; v. 298, p. 30-67, OCT 15 2021.
• Web of Science Citations: 0

Abstract

In this paper we consider the semilinear damped wave problem of the form [(alpha(t)u(t))(t) - beta(t)Delta u + gamma(t)u(t) + delta(t)u = beta(t) f(u), x is an element of Omega, t > tau, u(x, t) = 0, x is an element of partial derivative Omega, t >= tau, u(x, tau) = u(tau) (x), u(t)(x, tau) = v(tau) (x), x is an element of Omega, where Omega is a bounded smooth domain in R-N, N >= 3, tau is an element of R, f is a real valued function of a real variable with some suitable conditions of growth, regularity and dissipativity, and alpha, beta, gamma and delta are continuous real valued functions of a real variable with some suitable conditions of growth, regularity and signs. Using rescaling of time we prove existence, regularity, gradient-like structure, upper and lower semicontinuity of the pullback attractors for the evolution processes associated with this boundary initial value problem in a suitable phase space. (C) 2021 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 19/26841-8 - Study of non-autonomous semilinear parabolic and hyperbolic problems
• Grantee: Marcelo José Dias Nascimento
• Support Opportunities: Regular Research Grants
• FAPESP's process: 19/04476-6 - Dynamic systems in infinite dimensional spaces
• Grantee: Gleiciane da Silva Aragão
• Support Opportunities: Regular Research Grants