Diffraction of singularities for the wave equation on manifolds with corners
By: Richard Melrose & András Vasy & Jared Wunsch
Series: Astérisque -- Vol. 351; Astérisque -- 351.
Publisher: Société mathématique de France
Published: 2013
Place of publication: Paris
Language: eng
Number of pages: 135
ISBN-13: 9782856293676
Subjects: Wave equation; Manifolds (Mathematics); Singularities (Mathematics)
Description: "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."--Page 4 of cover.
Notes: Includes bibliographical references (pages [133]-135).

Abstract also in French.