Electron. J. Diff. Eqns., Vol. 1995(1995), No. 17, pp 1-14.

Reflectionless Boundary Propagation Formulas for Partial Wave Solutions to the Wave Equation

Jaime Navarro & Henry A. Warchall

We consider solutions to the wave equation in 3+1 spacetime dimensions whose data is compactly supported at some initial time. For points outside a ball containing the initial support, we develop an outgoing wave condition, and associated one-way propagation formula, for the partial waves in the spherical-harmonic decomposition of the solution. The propagation formula expresses the $l$-th partial wave at time t and radius a in terms of order-l radial derivatives of the partial wave at time $t-\Delta t$ and radius $a-\Delta t$. The boundary propagation formula can be applied to any differential equation that is well-approximated by the wave equation outside a fixed ball.

Submitted May 20, 1994. Published November 28, 1995.
Math Subject Classification: 35L05, 35L15, 35C10, 35A35, 35A22.
Key Words: One-sided wave propagation, Wave equation, Reflectionless boundary conditions, Partial waves, Spherical-harmonic decomposition, Open-space boundary conditions.

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Jaime Navarro
Universidad Autonoma Metropolitana
Unidad Azcapotzalco, Division de Ciencias Basicas
Apdo. Postal 16-306, Mexico D.F. 02000, Mexico
e-mail: jnfu@hp9000a1.uam.mx
Henry A. Warchall
Department of Mathematics, University of North Texas
Denton TX 76203-5116, USA
e-mail: hankw@unt.edu

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