Propagation of singularities for the wave equation on conic manifolds
Analysis of PDEs
2007-05-23 v1 Mathematical Physics
Classical Analysis and ODEs
math.MP
Abstract
For the wave equation associated to the Laplacian on a compact manifold with boundary with a conic metric (with respect to which the boundary is metrically a point) the propagation of singularities through the boundary is analyzed. Under appropriate regularity assumptions the diffracted, non-direct, wave produced by the boundary is shown to have Sobolev regularity greater than the incoming wave.
Cite
@article{arxiv.math/0111255,
title = {Propagation of singularities for the wave equation on conic manifolds},
author = {Richard Melrose and Jared Wunsch},
journal= {arXiv preprint arXiv:math/0111255},
year = {2007}
}