Critical curve for a weakly coupled system of semilinear σ-evolution equations with frictional damping

Abstract

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.