Propagation of singularities for the wave equation on edge manifolds

Richard Melrose*, András Vasy, Jared Wunsch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)109-193
Number of pages85
JournalDuke Mathematical Journal
Volume144
Issue number1
DOIs
StatePublished - Jul 15 2008

ASJC Scopus subject areas

  • Mathematics(all)

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