## Rocky Mountain Journal of Mathematics

### Distributional analysis of radiation conditions for the $3+1$ wave equation

#### 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.

#### Article information

Source
Rocky Mountain J. Math., Volume 49, Number 1 (2019), 1-27.

Dates
First available in Project Euclid: 10 March 2019

https://projecteuclid.org/euclid.rmjm/1552186949

Digital Object Identifier
doi:10.1216/RMJ-2019-49-1-1

Mathematical Reviews number (MathSciNet)
MR3921864

Zentralblatt MATH identifier
07036616

#### Citation

Ellison, J.A.; Heinemann, K.A.; Lau, S.R. Distributional analysis of radiation conditions for the $3+1$ wave equation. Rocky Mountain J. Math. 49 (2019), no. 1, 1--27. doi:10.1216/RMJ-2019-49-1-1. https://projecteuclid.org/euclid.rmjm/1552186949

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