2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98353The 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.23 pages, 1 figureAnalysis of PDEsClassical Analysis and ODEs35L15; 35B45text