Singular perturbation of a linear hyperbolic system

Abstract

This paper carries out a singular perturbation analysis of a linear hyperbolic system in two dependent and two independent variables. By estimating the remainder terms, a formal approximation to the solution of the system is shown to provide a valid approximation to the exact solution. A number of interesting phenomena arise from the analysis. In particular (i) two different types of boundary layer terms arise, each with the same scale, (ii) the off-diagonal elements in the coefficient matrix prove to be relatively unimportant and (iii) the relationship between the first order system and a second order scalar hyperbolic equation to which it may be reduced in special circumstances involves restrictions on the coefficients requiring interpretation and further examination.

Keywords:

• Singular perturbation
• linear hyperbolic system

AMS(MOS)::

• L99
• L15