Posing an inverse problem for the Helmholtz equation in a half plane

• Autores: Frank Penzel
• Localización: Mathematische Nachrichten, ISSN 0025-584X, Vol. 280, Nº. 9-10, 2007, págs. 1200-1204
• Idioma: inglés
• DOI: 10.1002/mana.200510546
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• Resumen

  • In this paper we shall define an inverse problem for the Helmholtz equation with imaginary part of the wave number being positive. The Cauchy data are known on the boundary of the half plane, but it is not known where the half axis, lying vertically in the upper half plane, is situated. It is known that the Dirichlet data on that unknown boundary is vanishing.

    The direct problem may be reduced to the solution of a boundary value problem in the plane where the boundary consists of two vertically lying half axes in the plane. We shall present the explicit solution of the direct problem and we shall discuss conditions on the Cauchy data for solvability of the inverse problem