Boundary conditions for coupled quasilinear wave equations with application to isolated systems.

H.O. KREISS, O. REULA, O. SARBACH, J. WINICOUR

COMMUNICATIONS IN MATHEMATICAL PHYSICS

SPRINGER

Lugar: New York; Año: 2009 vol. 289 p. 1099 - 1129

0010-3616

We consider the initial-boundary value problem for systems of quasilinear wave equations on domainsof the form [0, T]×, where  is a compact manifold with smooth boundaries @. By usingan appropriate reduction to a first order symmetric hyperbolic system with maximal dissipativeboundary conditions, well posedness of such problems is established for a large class of boundaryconditions on @. We show that our class of boundary conditions is sufficiently general to allow fora well posed formulation for different wave problems in the presence of constraints and artificial,nonreflecting boundaries, including Maxwell’s equations in the Lorentz gauge and Einstein’s gravitationalequations in harmonic coordinates. Our results should also be useful for obtaining stablefinite-difference discretizations for such problems.