Diffraction of singularities for the wave equation on manifolds with corners
"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, which are not propagated alo...
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Paris
Société Mathématique de France
2013
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| Schriftenreihe: | Astérisque
351 |
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| Online Zugang: | Inhaltstext |
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Tag hinzufügen | Zusammenfassung: | "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, which 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."--Page 4 of cover Introduction -- Geometry : metric and Laplacian -- Bundles and bicharacteristics -- Edge-b calculus -- Differential-pseudodifferential operators -- Coisotropic regularity and non-focusing -- Edge propagation -- Propagation of fiber-global coisotropic regularity -- Geometric theorem |
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| Beschreibung: | Zsfassung in engl. und frz. Sprache Zsfassung in franz. Sprache u.d.T.: Diffraction des singularités de l'équation d'onde sur les variétés à coins Zsfassung in engl. und frz. Sprache |
| Beschreibung: | VI, 135 S. graph. Darst. |
| ISBN: | 9782856293676 978-2-85629-367-6 |