Initial-Boundary Value Problems for Linear Hyperbolic System

Abstract

We discuss and interpret a theory developed by Kreiss and others for studying the suitability of boundary conditions for linear hyperbolic systems of partial differential equations. The existing theory is extremely technical. The present discussion is based on the characteristic variety of the system. The concept of characteristic variety leads to (1) a physical interpretation of the theory in terms of wave propagation, and (2) a physical and geometrical method for visualizing the algebraic structure of the system. The great complexity of the theory is caused by certain aspects of this structure. We also point out connections between the above work and a corresponding theory regarding the stability of finite difference approximations.