Local energy decay for the wave equation with nonlinear time dependent   damping
  This paper addresses a wave equation on a exterior domain in R^{d}(d odd) with nonlinear time dependent dissipation. Under a microlocal geometric condition we prove that the decay rates of the local energy functional are obtained by solving a nonlinear non-autonomous differential equation. 
A. Bchatnia and M. Daoulatli
math.OC math.AP