Weighted L2-estimates of solutions for damped wave equations with variable coefficients
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The authors establish weighted L2-estimates of solutions for the damped wave equations with variable coefficients u tt − divA(x)∇u+au t = 0 in ℝ n under the assumption a(x) ≥ a0[1+ρ(x)]−l, where a0 > 0, l < 1, ρ(x) is the distance function of the metric g = A−1(x) on ℝ n . The authors show that these weighted L2-estimates are closely related to the geometrical properties of the metric g = A−1(x).
KeywordsDistance function of a metric Riemannian metric wave equation with variable coefficients weighted L2-estimate
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