Wave Propagation at Computational Domain Boundaries
Henry A. Warchall · Communications in Partial Differential Equations · 1991
We study multiple-time inital value problems for linear wave equations that model a situation common in numerial simulation of solutions to hyperbolic partial differential equaitons formulated on unbounded spatial domains. It is shown that the restriction of the solution to a convex spatial domain is determined by data inside the domain alone at an earlier time, provided that the support of the data at some (perhaps ancient) initial time was contained in the domain. More precisely, it is shown that if the initial (timet$sub:0(timet$sub:0$esub:) data has support in the open convex set Ωif x is in the closure Ω and if t$sub:0$esub:<t$sub:1$esub: