α-contractions and attractors for dissipative semilinear hyperbolic equations and systems

Abstract

In this paper we discuss the existence of compact attractor for the abstract semilinear evolution equation u=Au+f(t, u); the results are applied to damped partial differential equations of hyperbolic type. Our approach is a combination of Liapunov method with the theory of α-eontractions. © 1991 Fondazione Annali di Matematica Pura ed Applicata.