L'équation de Helmholtz avec impédance dans un demi-espace

Translated title of the contribution: The Helmholtz equation with impedance in a half-space

Mario Durán, IGNACIO PATRICIO PEDRO MUGA URQUIZA, Jean Claude Nédélec

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

In this Note we obtain existence and uniqueness results for the Helmholtz equation in the half-space ℝ+ 3 with an impedance or Robin boundary condition. Basically, we follow the procedure we have already used in the bi-dimensional case (the half-plane). Thus, we compute the associated Green's function with the help of a double Fourier transform and we analyze its far field in order to obtain radiation conditions that allow us to prove the uniqueness of an outgoing solution. Again, these radiation conditions are somewhat unusual due to the appearance of a surface wave guided by the boundary. An integral representation of the solution is presented by means of the Green's function and the boundary data.

Translated title of the contributionThe Helmholtz equation with impedance in a half-space
Original languageFrench
Pages (from-to)561-566
Number of pages6
JournalComptes Rendus Mathematique
Volume341
Issue number9
DOIs
StatePublished - 1 Nov 2005

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