Removing small divisors in the method of characteristic

Abstract

The traditional method of characteristics applied to linear systems ofconservation laws with “clore” speeds of propagation could lead to expressions of solutions which contain small divisors. These could cause dificulty in compuations We propose to eliminate thew small divisors by developing a uniform representation for solutions of a linear degenerate systems of conservation laws. The uniform representation is achieved by global triangularization of matrix fnctions and the calculus of finite differences. We also obtain the asymptotic behaviour for large times t of solutions of degenerate hyperbolic systems among other by products.

Keywords:

• methods of characteristics
• degenerate hyperbolic systems
• triangularization
• matrix functions