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27 de julio de 2024
High frequency limit of the Helmholtz equations.
| Título inglés | High frequency limit of the Helmholtz equations. |
|---|---|
| Título español | Límite de alta frecuencia de las ecuaciones de Helmholtz. |
| Autor/es | Benamou, Jean-David ; Castella, François ; Katsaounis, Theodoros ; Perthame, Benoit |
| Organización | INRIA, Le Chesnay, Francia;CNRS - IRMAR, Univ. Rennes 1, Rennes, Francia;IACM-Forth, Heraklion Creta, Grecia |
| Revista | 0213-2230 |
| Publicación | 2002, 18 (1): 187-209, 19 Ref. |
| Tipo de documento | articulo |
| Idioma | Inglés |
| Resumen inglés | We derive the high frequency limit of the Helmholtz equations in terms of quadratic observables. We prove that it can be written as a stationary Liouville equation with source terms. Our method is based on the Wigner Transform, which is a classical tool for evolution dispersive equations. We extend its use to the stationary case after an appropriate scaling of the Helmholtz equation. Several specific difficulties arise here; first, the identification of the source term ( which does not share the quadratic aspect) in the limit, then, the lack of L2 bounds which can be handled with homogeneous Morrey-Campanato estimates, and finally the problem of uniqueness which, at several stage of the proof, is related to outgoing conditions at infinity. (A) |
| Clasificación UNESCO | 120220 |
| Palabras clave español | Ecuación de Helmholtz ; Ecuación de Liouville ; Optica geométrica ; Transformada de Wigner |
| Código MathReviews | MR1924691 |
| Código Z-Math | Zbl 1090.35165 |
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