Attractors for processes on time-dependent spaces

Abstract

The goal of this master’s degree dissertation is to study the asymptotic behavior of non-autonomous hyperbolic partial differential equations with time-dependent coefficients. In order to achieve that, we introduce the notion of pullback attractors for processes on time-dependent spaces, where the solution operator is a family of maps U(t, τ) : X τ → X t , t ≥ τ ∈ R acting on a time-dependent family of spaces X t . Furthermore, we exploiting the minimality with respect to the pullback attraction property and the existence of those attractors. Finally, we applied the abstract results on existence of pullback attractors to study the long term behavior of a damped wave equation with time-dependent speed of propagation.