The Helmholtz equation in a locally perturbed half-plane with passive boundary

Mario Durán, Ignacio Muga, Jean Claude Nédélec

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19 Scopus citations


In this article, we study the existence and uniqueness of outgoing solutions for the Helmholtz equation in locally perturbed half-planes with passive boundary. We establish an explicit outgoing radiation condition which is somewhat different from the usual Sommerfeld's one due to the appearance of surface waves. We work with the help of Fourier analysis and a half-plane Green's function framework. This is an extended and detailed version of the previous article Durán et al. (2005, The Helmholtz equation with impedance in a half-plane. C. R. Acad. Sci. Paris, Ser. I, 340, 483-488).

Original languageEnglish
Pages (from-to)853-876
Number of pages24
JournalIMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Issue number6
StatePublished - Dec 2006


  • Green's function
  • Helmholtz equation on half-plane
  • Radition condition


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