Electronic Journal of Differential Equations,
Vol. 1995(1995), No. 17, pp 1--14.
Title: Reflectionless Boundary Propagation Formulas
for Partial Wave Solutions to the Wave Equation
Authors: Jaime Navarro (Univ. Uatonoma, Mexico)
Henry A. Warchall (Univ. of North Texas, Denton, TX, USA)
Abstract: 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.