Uniform asymptotics of solutions of the wave operator with meromorphic coefficients

Abstract

We study the problem of wave propagation in the medium whose velocity characteristics change under an external impact. We will study a three-dimensional case. The aim of our study is constructing the asymptotic of the solution for the wave operator with a variable time depended coefficient of the Laplacian at infinity. The case of meromorphic and holomorphic coefficients is considered.