Asymptotic properties of solutions to weakly dissipative wave equations below scaling

Details Asymptotic properties of solutions to weakly dissipative wave equations below scaling Asymptotic properties of solutions to weakly dissipative wave equations below scaling

2004-06-25

arxiv.org/abs/math/0406515v2

Mathematics

Analysis of PDEs

23 pages, 1 figure

Scientific paper

The aim of this paper is to understand the influence of a dissipative term which is small in the sense that it is asymptotically below scaling on the asymptotic properties of solutions. A diagonalization procedure is applied in order to construct the main terms of the solution representation and this information is used to prove $L^p$--$L^q$ decay estimates. Furthermore, the question of sharpness is considered and formulated in terms of a modified scattering theory.

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