Singular limits of quasilinear hyperbolic systems in a bounded domain of R³ with applications to Maxwell’s equations

Albert Milani

Vol. 116 (1985), No. 1, 111–129

DOI: 10.2140/pjm.1985.116.111

Abstract

We establish a singular perturbation result for quasi-linear hyperbolic systems in a bounded domain of R³, depending on a small parameter. We prove and estimate the rate of convergence, as the parameter tends to zero, of uniformly stable solutions of the complete system to a solution of the reduced system. This result is then applied to the study of the convergence of the complete Maxwell equations to the quasi-stationary ones.

Mathematical Subject Classification 2000

Primary: 35L70

Secondary: 35B25

Milestones

Received: 25 April 1983

Published: 1 January 1985