Work

Model boundary value problem for the Helmholtz equation in a nonconvex angle with periodic boundary data

Year: 2025

Type: article

Abstract: In the present 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 functional class and give an explicit formula for it in the form of the Sommerfeld integral. The method of complex characteristics (Komech and Merzon in Stationary Diffraction by Wedges, Lect. Notes Math., vol. 2249, Springer, Berlin, 2019 ) is used.

Source: Boundary Value Problems

DOI: 10.1186/s13661-025-02022-w

Authors: A. Merzon, P. Zhevandrov, M. I. Romero Rodríguez, J. E. De la Paz Méndez

Institutions: Universidad Michoacana de San Nicolás de Hidalgo, Military University Nueva Granada, Universidad Autónoma de Guerrero

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,890

Funders: Universidad Militar Nueva Granada, Sistema Nacional de Investigadores