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<p>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.&#xa0;2249, Springer, Berlin, <CitationRef CitationID="CR17">2019</CitationRef>) is used.</p>

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

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  • 发表日期：

    2025年2月18日

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

摘要

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.