Abstract
Properties concerning the decay of solutions to the linear damped wave equation are essential tools for studying decay and long time behaviour of solutions to their semilinear and nonlinear counterparts. In this article we extend and improve classical estimates for linear damped wave equations obtained by Matsumura. Our main tool is the decay character of initial data, which has been used to prove similar results for other dissipative equations. We then apply these estimates to recover and improve decay results for the damped wave equation with absorption for initial data in different function spaces.
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