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Asymptotic properties of solutions to weakly dissipative wave equations below scaling

Jens Wirth
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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 $L^p$--$L^q$ decay estimates. Furthermore, the question of sharpness is considered and formulated in terms of a modified scattering theory.

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Jens Wirth. 2004-07-27. Asymptotic properties of solutions to weakly dissipative wave equations below scaling. https://arxiv.org/abs/math/0406515

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