Weakly coupled systems of semi-linear wave equations with memory-type dissipation, different power nonlinearities and different regularity of data

Wenhui Chen, Abdelhamid Mohammed Djaouti

Published 2018-07-17Version 1

We consider the Cauchy problem for semi-linear wave equations with memory-type dissipation. Taking into confederation the point-wise estimate of solutions to the corresponding linear problem in the Fourier space, we get the energy estimates. By introducing a set of time-weighted Sobolev spaces and applying the contracting mapping theorem, we study the global existence of small data solutions to the Cauchy problem for weakly coupled systems of semi-linear wave equations with memory-type dissipation, where data are supposed to belong to different classes of regularity.