Weighted L-estimates for Dissipative Wave Equations with Variable Coefficients

@inproceedings{Yordanov2007WeightedLF,
  title={Weighted L-estimates for Dissipative Wave Equations with Variable Coefficients},
  author={Borislav Yordanov},
  year={2007}
}
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… CONTINUE READING