CRITICAL CURVE FOR A WEAKLY COUPLED SYSTEM OF SEMILINEAR sigma-EVOLUTION EQUATIONS WITH FRICTIONAL DAMPING

摘要

We are interested in studying the Cauchy problem for a weakly coupled system of semilinear sigma-evolution equations with frictional damping. The main purpose of this paper is two-fold. We would like to not only prove the global (in time) existence of small data energy solutions but also indicate the blow-up result for Sobolev solutions when sigma is assumed to be any fractional number. Moreover, some further generalizations will be also discussed in the present paper.