Explicit solution of a Dirichlet problem in nonconvex angle

A. Merzon ; P. Zhevandrov ; J. E. De la Paz Méndez ; M. I. Romero Rodríguez

Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 68 (2022) no. 4, pp. 653-670.

Résumé

In the present work, we give an explicit solution of the Dirichlet boundary-value problem for the Helmholtz equation in a nonconvex angle with periodic boundary data. We present uniqueness and existence theorems in an appropriate functional class and we give an explicit formula for the solution in the form of the Sommerfeld integral. The method of complex characteristics [14] is used.

Détail

Keywords: Helmholtz equation, nonconvex angle, Sommerfeld integral, method of complex characteristics.

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