Asymptotics of the scattering operator for the wave equation in a singularly perturbed domain

Аннотация

A family of Cauchy-Dirichlet problems for the wave equations in unbounded domains $\Lambda_{\varepsilon}$ is considered (here $\varepsilon\ge 0$ is a small parameter); a scattering operator $\mathbb{S}_{\varepsilon}$ is associated with each domain $\Lambda_\varepsilon$. For $\varepsilon>0$ the boundaries of $\Lambda_{\varepsilon}$ are smooth, whilw the boundary of the limit domain $\Lambda_{0}$ contains a conical point. The asymptotics of $\mathbb{S}_{\varepsilon}$ as $\varepsilon\to 0$ is determined. Bibliography: 11 titles.