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.
Citation
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
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