Asymptotic properties of solutions to weakly dissipative wave equations below scaling
Jens Wirth
Abstract
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 Lp--Lq decay estimates. Furthermore, the question of sharpness is considered and formulated in terms of a modified scattering theory.
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