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.