Strichartz type estimates for the damped wave equation and their application (Regularity and Singularity for Partial Differential Equations with Conservation Laws)

Abstract

In this study, the Cauchy problem for the damped wave equation is considered. Solutions to the homogeneous damped wave equation are decomposed into the heat part and wave part. The decomposition implies that the solution behaves not only as a solution of a heat equation for t →, ∞ but also as a solution of a wave equation near t = 0. In this paper, based on the above results, we prove time global Strichartz type estimates for two and three dimensions. Furthermore using these estimates, we propose some well-posedness theorems for the nonlinear damped wave equation in the energy class.