The aim of this paper is to understand the influence of a dissipative termwhich is small in the sense that it is asymptotically below scaling on theasymptotic properties of solutions. A diagonalization procedure is applied in order to construct the main termsof the solution representation and this information is used to prove$L^p$--$L^q$ decay estimates. Furthermore, the question of sharpness isconsidered and formulated in terms of a modified scattering theory.
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机译：本文的目的是要了解耗散项的影响，该耗散项在解决方案的渐近性质上渐近低于缩放的意义上。应用对角化程序以构造解表示的主要项，并且该信息用于证明$ L ^ p $-$ L ^ q $衰减估计。此外，根据改进的散射理论考虑并提出了清晰度问题。
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