Higher order energy decay for damped wave equations with variable coefficients

Under appropriate assumptions the higher order energy decay rates for the damped wave equations with variable coefficients c(x)utt−div(A(x)∇u)+a(x)ut=0c(x)utt−div(A(x)∇u)+a(x)ut=0 in RnRn are established. The results concern weighted (in time) and pointwise (in time) energy decay estimates. We also obtain weighted L2L2 estimates for spatial derivatives.