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

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.