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 |
Acceso al artículo completo |