Model BVP problem for the Helmhotz equation in a nonconvex angle with periodic boundary data

TL;DR

This paper addresses the Dirichlet problem for the Helmholtz equation in a nonconvex angle with periodic boundary data, providing existence, uniqueness, and an explicit solution formula using complex characteristics.

Contribution

It introduces a novel approach to solving the Helmholtz equation in nonconvex angles with periodic data, including explicit solution representation.

Findings

Existence and uniqueness of solutions proven

Explicit Sommerfeld integral formula derived

Method of complex characteristics applied

Abstract

In the presented work, we solve the Dirichlet boundary problem for the Helmholtz equation in an exterior angle with periodic boundary data. We prove the existence and uniqueness of solution in an appropriate funcional class and we give an explicit formula for it in the form of the Sommerfeld integral. The method of complex characteristics [17] is used.