15 July 2008 Propagation of singularities for the wave equation on edge manifolds
Richard Melrose, András Vasy, Jared Wunsch
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Duke Math. J. 144(1): 109-193 (15 July 2008). DOI: 10.1215/00127094-2008-033


We investigate the geometric propagation and diffraction of singularities of solutions to the wave equation on manifolds with edge singularities. This class of manifolds includes, and is modeled on, the product of a smooth manifold and a cone over a compact fiber. Our main results are a general diffractive theorem showing that the spreading of singularities at the edge only occurs along the fibers and a more refined geometric theorem showing that for appropriately regular (nonfocusing) solutions, the main singularities can only propagate along geometrically determined rays. Thus, for the fundamental solution with initial pole sufficiently close to the edge, we are able to show that the regularity of the diffracted front is greater than that of the incident wave


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Richard Melrose. András Vasy. Jared Wunsch. "Propagation of singularities for the wave equation on edge manifolds." Duke Math. J. 144 (1) 109 - 193, 15 July 2008. https://doi.org/10.1215/00127094-2008-033


Published: 15 July 2008
First available in Project Euclid: 2 July 2008

zbMATH: 1147.58029
MathSciNet: MR2429323
Digital Object Identifier: 10.1215/00127094-2008-033

Primary: 35A21 , 35L05 , 58J47

Rights: Copyright © 2008 Duke University Press


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Vol.144 • No. 1 • 15 July 2008
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