We are interested in studying the Cauchy problem for a weakly coupled system of semilinear -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 is assumed to be any fractional number. Moreover, some further generalizations will be also discussed in the present paper.
"Critical curve for a weakly coupled system of semilinear -evolution equations with frictional damping." Rocky Mountain J. Math. 52 (1) 299 - 321, February 2022. https://doi.org/10.1216/rmj.2022.52.299