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

We consider the acoustic propagator A = - del.c(2)del in the strip Omega={( x,z)is an element of R-2\0<z<H} with finite width H > 0. The celerity c dep ends for large \x\ only on the variable z and describes the stratification of Omega: it is assumed to be in L-infinity(Omega), bounded from below by c (min) > 0, such that there exists M > 0 with c(x, z) = c(1)(Z) if X < - M a nd c(x, z) = c(2)(z) if x > M. We look at the propagator A as a 'perturbati on' of the free propagators A(j) in Omega associated to the Velocities c(j) , j = 1,2, and implement a 'perturbative' method, adapting ideas of Majda a nd Vainberg. The spectrum of A is defined in section 2, a limiting absorpti on principle is proved in section 3 outside of a countable set Gamma(A). Th e points of Gamma(A) can only accumulate at the left of the thresholds of t he free propagators. The needed material about A(j), xj = 1, 2, and some te chnical estimates for A are given in Appendix. (C) 1998 B. G. Teubner Stutt gart-John Wiley & Sons, Ltd.