Weighted L-estimates for Dissipative Wave Equations with Variable Coefficients
نویسندگان
چکیده
We establish weighted L2-estimates for the wave equation with variable damping utt −∆u+ aut = 0 in R, where a(x) ≥ a0(1+ |x|)−α with a0 > 0 and α ∈ [0, 1). In particular, we show that the energy of solutions decays at a polynomial rate t−(n−α)/(2−α)−1 if a(x) ∼ a0|x|−α for large |x|. We derive these results by strengthening significantly the multiplier method. This approach can be adapted to other hyperbolic equations with damping.
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