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Analyse haute fréquence de l'équation de Helmholtz avec terme source

Abstract : We study the high frequency limit of the Helmholtz equation with source term in the case when the frequency of the oscillations due to the source is the same as that of the eigen modes of the Helmholtz operator, so as to create resonant ineractions. We quantify the asymptotic transport of the energy using Wigner measures (or semiclassical measures).
We study two different situations: the case of two point sources (for which we restrict ourselves to a constant index of refraction), and the case of a refraction index that is discontinuous along an interface between two unbounded inhomogeneous media.
In both cases, we prove that, under some geometric hypotheses, the Wigner measure is the integral along the rays of geometric optics and up to infinite time, of an energy source that measures the resonant interactions between the source and the solution.
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Contributor : Elise Fouassier <>
Submitted on : Wednesday, June 14, 2006 - 1:07:28 PM
Last modification on : Thursday, January 7, 2021 - 4:22:15 PM
Long-term archiving on: : Monday, April 5, 2010 - 10:49:28 PM


  • HAL Id : tel-00080011, version 1


Elise Fouassier. Analyse haute fréquence de l'équation de Helmholtz avec terme source. Mathématiques [math]. Université Rennes 1, 2005. Français. ⟨tel-00080011⟩



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