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2019 Distributional analysis of radiation conditions for the $3+1$ wave equation
J.A. Ellison, K.A. Heinemann, S.R. Lau
Rocky Mountain J. Math. 49(1): 1-27 (2019). DOI: 10.1216/RMJ-2019-49-1-1

Abstract

Consider the Cauchy problem for the ordinary 3+1 wave equation. Reduction of the spatial domain to a half-space involves an exact radiation boundary condition enforced on a planar boundary. This boundary condition is most easily formulated in terms of the tangential-Fourier and time-Laplace transform of the solution. Using the Schwartz theory of distributions, we examine two other formulations: (i) the nonlocal spacetime form and (ii) its three-dimensional (tangential/time) Fourier transform. The spacetime form features a convolution between two tempered distributions.

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J.A. Ellison. K.A. Heinemann. S.R. Lau. "Distributional analysis of radiation conditions for the $3+1$ wave equation." Rocky Mountain J. Math. 49 (1) 1 - 27, 2019. https://doi.org/10.1216/RMJ-2019-49-1-1

Information

Published: 2019
First available in Project Euclid: 10 March 2019

zbMATH: 07036616
MathSciNet: MR3921864
Digital Object Identifier: 10.1216/RMJ-2019-49-1-1

Subjects:
Primary: 35L05, 35L50, 60E05, 65M99

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 1 • 2019
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