Weakly Coupled Systems of Semilinear Effectively Damped Waves with Different Time-Dependent Coefficients in the Dissipation Terms and Different Power Nonlinearities

Abstract

We study the global existence of small data solutions to the Cauchy problem for the coupled system of semilinear damped wave equations with different effective dissipation terms and different exponents of power nonlinearities. The data are supposed to belong to different classes of regularity. We will show the interaction of the exponents p and q on the one hand and on the other hand the interaction of the dissipation terms b 1 (t)u t and b 2 (t)v t .