Modified scattering for a wave equation with weak dissipation

Details Modified scattering for a wave equation with weak dissipation Modified scattering for a wave equation with weak dissipation

2005-09-10

arxiv.org/abs/math/0509229v1

Mathematics

Analysis of PDEs

7 pages

Scientific paper

We consider the Cauchy problem for the weakly dissipative wave equation $$ \square u+\frac\mu{1+t} u_t=0 $$ with parameter $\mu\ge2$. 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.

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