The authors establish weighted L^2-estimates of solutions for the damped wave equations with variable coefficients utt-div A(x)▽u + au_t = 0 in IR^nunder the assumption a(x) ≥ a_0[1 + ρ(x)]^(-l),where a_0 > 0, l...The authors establish weighted L^2-estimates of solutions for the damped wave equations with variable coefficients utt-div A(x)▽u + au_t = 0 in IR^nunder the assumption a(x) ≥ a_0[1 + ρ(x)]^(-l),where a_0 > 0, l < 1, ρ(x) is the distance function of the metric g = A^(-1)(x) on IR^n. The authors show that these weighted L^2-estimates are closely related to the geometrical properties of the metric g = A^(-1)(x).展开更多
基金supported by the National Science Foundation of China under Grant Nos.61573342,61473126the Key Research Program of Frontier Sciences,Chinese Academy of Sciences,under Grant No.QYZDJ-SSWSYS011 the Fundamental Research Funds for the Central Universities
文摘The authors establish weighted L^2-estimates of solutions for the damped wave equations with variable coefficients utt-div A(x)▽u + au_t = 0 in IR^nunder the assumption a(x) ≥ a_0[1 + ρ(x)]^(-l),where a_0 > 0, l < 1, ρ(x) is the distance function of the metric g = A^(-1)(x) on IR^n. The authors show that these weighted L^2-estimates are closely related to the geometrical properties of the metric g = A^(-1)(x).
