Asymptotic completeness for acoustic propagators in perturbed stratified media

Asymptotic behavior of stationary solutions to elastic wave equations in a perturbed half‐space in ℝ3

“…As an consequence of Lemma 6.2, we can show that for G ∈ C ∞ 0 (R + ), (L + i) −1 (W ± −  )G(L 0 )P ± is a compact operator. Arguing as in Enss [28] and Perry [29] as in the proof of (4.3) of Kadowaki [27], we obtain the asymptotic completeness.…”

“…Theorem 5.4 can be proved in almost the same manner as in Kadowaki [27]. Here, we give the sketch only.…”

Low and High Energy Resolvent Estimates for Wave Propagation in Stratified Media and Their Applications

“…But it seems that there is little literature dealing with dissipative wave equations in stratified media (cf. [14] or Kadowaki [4]). …”

“…Mourre [12]) to the original operator, L 0 , we construct the conjugate operator by using generators of dailation in R n+1 and exterior domains of ball in R n together with the generalized Fourier transform for L 0 (cf. Kadowaki [4]). Then we fail to get the Mourre's estimates on the neighborhood of thresholds of L 0 .…”

Low Energy Resolvent Estimates for Acoustic Propagators in Perturbed Stratified Media

“…Kadowaki [1] has showed Asymptotic completeness for acoustic wave equation in perturbed stratified media by using the eigenfunction expansion theorem of (1.2) (cf. Wilcox [8]).…”