ACTA issues

Well-posedness and decay estimates for a Petrovsky system by a semigroup approach

Vilmos Komornik

Acta Sci. Math. (Szeged) 60:3-4(1995), 451-466

Abstract. The present paper follows a previous work where energy decay estimates were obtained for strong solutions of a Petrovsky system with nonlinear internal damping. The well-posedness of the problem and the estimates were obtained by using the Faedo--Galerkin method. In this paper we apply a semigroup approach. This also allows us to consider weak solutions and to remove some unnatural technical assumptions concerning the nonlinearities. Moreover, this method leads to shorter proofs.

AMS Subject Classification (1991): 93C20, 93D15, 35Q72

Received November 7, 1994. (Registered under 5644/2009.)