$L^p$--$L^q$ decay estimates for wave equations with monotone   time-dependent dissipation
  This expository article is intended to give an overview about recently achieved results on asymptotic properties of solutions to the Cauchy problem $u_{tt}-\Delta u+b(t)u_t =0,\qquad u(0,\cdot)=u_1,\quad \mathrm{D}_tu(0,\cdot)=u_2$ for a wave equation with time-dependent dissipation term. The results are based on structural properties of the Fourier multipliers representing its solution. The article explains the general philosophy behind the approach. 
Michael Reissig and Jens Wirth