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• W3021972052 abstract "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" @default.
• W3021972052 created "2020-05-13" @default.
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• W3021972052 date "2008-07-15" @default.
• W3021972052 modified "2023-10-15" @default.
• W3021972052 title "Propagation of singularities for the wave equation on edge manifolds" @default.
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• W3021972052 doi "https://doi.org/10.1215/00127094-2008-033" @default.
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