Weighted L2-estimates of solutions for damped wave equations with variable coefficients

    The authors establish weighted L²-estimates of solutions for the damped wave equations with variable coefficients u_tt−divA(x)∇u+a(x)u_t=0 in Rn under some assumptions on the damping a(x). The authors show that these weighted L²-estimates are closely related to the geometrical properties of the metric determined by A(x). Some examples are given about applications of those L²-estimates in obtaining stabilization properties of wave equations.