Diffraction of singularities for the wave equation on manifolds with corners / Richard Melrose, András Vasy, Jared Wunsch
Type de document : MonographieCollection : Astérisque, 351Langue : anglais.Pays: France.Éditeur : Paris : Société Mathématique de France, cop. 2013Description : 1 vol. (VI-136 p.) ; 24 cmISBN: 9782856293676.ISSN: 0303-1179.Bibliographie : Bibliogr. p. 133-135. Index.Sujet MSC : 35L05, PDEs - Hyperbolic equations and hyperbolic systems, Wave equation58J47, Global analysis, analysis on manifolds - PDEs on manifolds; differential operators, Propagation of singularities; initial value problems on manifolds
78A45, Optics, electromagnetic theory - General, Diffraction, scatteringEn-ligne : SMF résumé
| Item type | Current library | Call number | Status | Date due | Barcode |
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Monographie
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CMI Salle 1 | Séries SMF 351 (Browse shelf(Opens below)) | Available | 09695-01 |
Bibliogr. p. 133-135. Index
We consider the fundamental solution to the wave equation on a manifold with corners of arbitrary codimension. If the initial pole of the solution is appropriately situated, we show that the singularities which are diffracted by the corners (i.e., loosely speaking, are not propagated along limits of transversely reflected rays) are smoother than the main singularities of the solution. More generally, we show that subject to a hypothesis of nonfocusing, diffracted wavefronts of any solution to the wave equation are smoother than the incident singularities. These results extend our previous work on edge manifolds to a situation where the fibers of the boundary fibration, obtained here by blowup of the corner in question, are themselves manifolds with corners. (Source : SMF)
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