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

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

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arXiv · 2208.13130

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

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

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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.

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A. Merzon, P. Zhevandrov, M. I. Romero Rodríguez, J. E. De la Paz Méndez. 2022-08-28. Model BVP problem for the Helmhotz equation in a nonconvex angle with periodic boundary data. https://arxiv.org/abs/2208.13130

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