A perturbative method for the spectral analysis of an acoustic multistratified strip

✍ Scribed by Elisabeth Croc; Yves Dermenjian

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 220 KB
• Volume: 21
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/(sici)1099-1476(199812)21:18<1681::aid-mma16>3.0.co;2-4

✦ Synopsis

We consider the acoustic propagator A"! ) c in the strip "+(x, z)31"0(z(H, with finite width H'0. The celerity c depends for large "x" only on the variable z and describes the stratification of : it is assumed to be in ¸( ), bounded from below by c '0, such that there exists M'0 with c(x, z)"c (z) if x(!M and c(x, z)"c (z) if x'M. We look at the propagator A as a 'perturbation' of the free propagators A H in associated to the velocities c H , j"1, 2, and implement a 'perturbative' method, adapting ideas of Majda and Vainberg. The spectrum of A is defined in section 2, a limiting absorption principle is proved in section 3 outside of a countable set (A). The points of (A) can only accumulate at the left of the thresholds of the free propagators. The needed material about A H , j"1, 2, and some technical estimates for A are given in Appendix.