Asymptotic Maslov’s method for shocks of conservation laws systems with quadratic flux

Abstract

In this work we apply the asymptotic method suggested by Maslov [1] to obtain the Hugoniot–Maslov chain for shock type solutions of conservation laws systems with quadratic flux. Additionally to the ODE infinite system that make up the chain, it was obtained an algebraic compatibility condition that must be satisfied by some of the coefficients of the asymptotic expansion of the shock solution. We give a new geometrical interpretation for this compatibility condition by means of certain singular surface whose projections represent time-dependent Hugoniot locus through the left limit state of the Shock.

Keywords:

• Conservation laws
• shock waves
• Hugoniot–Maslov chains
• Colombeau’s generalized functions
• Hugoniot locus
• generalized Riemann problem

AMS Subject Classifications:

• 35A20
• 35F55
• 35L67
• 46F30

Notes

No potential conflict of interest was reported by the authors.