Identifier: 2007-20
Author(s): S Lau
Title: On Partial Spherical Means Formulas and Radiation Boundary Conditions for the 3+1 Wave Equation
Page count: 31 pp.
Date: 2007-01-01
Abstract:
We derive various partial spherical means formulas for the 3+1 wave equation. Such formulas, considered earlier by Teng, involve only partial integration over solid angle in addition to history–dependent boundary terms, and are appropriate for faces, edges, and corners of “computational domains”. For example, a hemi- spherical means formula corresponds to a face (plane boundary). Exploiting the theory of wave front sets for linear operators developed by Hormander, Warchall has proved theorems which suggest the existence of “one–sided update formulas” for wave equations. We attempt to realize such an update formula via an explicit con- struction based on our hemispherical means formula. We focus on face points and plane boundaries, but also introduce one–fourth and one–eighth spherical means formulas with most of our arguments going through for a point located at either a domain edge or corner. Throughout our analysis we encounter a number of, we believe, heretofore unknown identities for classical solutions to the wave equation.
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