Asymptotic properties of solutions to weakly dissipative wave equations   below scaling
  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. 
Jens Wirth