Asymptotic Solutions of Hyperbolic Boundary Value Problems with Diffraction

Abstract

This paper concerns the propagation of analytic singularities in boundary value problems. We are mainly interested in the problem

$$( - \Delta + {\text{D}}_{\text{t}}^2){\text{u}}|{\text{A}}(\mathbb{R} \times \Omega )$$

((1.1))

$${{\text{u}}_{|\mathbb{R} \times \partial \Omega }}{\text{A}}(\mathbb{R} \times \partial \Omega )$$

((1.2))

where Ω, is an open subset of ℝ^n-1 with analytic boundary. The Dirichlet boundary condition (1.2) can be replaced by many others, in particular by the Neumann boundary condition

$${{\text{D}}_\nu }{{\text{u}}_{|\mathbb{R} \times \partial \Omega }}{\text{A}}(\mathbb{R} \times \partial \Omega )$$

((1.3))

.