Global solutions to the Cauchy problem for a system of damped wave equations

Abstract

The Cauchy problem to the system of nonlinear damped wave equations is treated. Several authors have shown existence and asymptotic behavior of global solutions to the above problem when the space dimension is not greater than three. We will show the existence and asymptotic behavior of global solutions to the problem with rapidly decaying initial data when the space dimension is greater than three, where we apply estimates in weighted Sobolev spaces of the above solution operator. Moreover, using the theory of modulation spaces introduced by Feitinger [4], we will also show the existence and asymptotic behavior of global solutions to the problem with slowly decaying initial data.