Modified scattering for a wave equation with weak dissipation

Abstract

We consider the Cauchy problem for the weakly dissipative wave equation $$\square u+\frac{\mu }{1+t}{u}_t=0$$ with parameter $\mu \ge 2$. Based on the explicit representations of solutions provided in [Math. Meth. Appl. Sci. 2004; {\bf 27}:101-124] sharp decay estimates for data from a dense subspace of the energy space are derived. Furthermore, sharpness is discussed in terms of a modified scattering theory.

7 pages