Regular by Pieces Kinematic Waves: Analysis of the Maslow I Chains

Abstract

An analytical study of the Maslov chain conditions for regular by pieces kinematics waves is performed. The constancy -along each one of the structured time intervals- of the rupture orders associated to the singular points is mathematically proved. Attention is then focused into the study of non-cero rupture orders and the remaining results are restricted to this area. The singular paths are then proved to be restricted to evolve in time along segments of characteristics lines. Significant simplifications are then performed into the Maslov chains. Some further developments lead to the conclusion that the simplified chain conditions can be solved as two independent iterative sequences of linear first order ordinary differential equations. Trough the totality of the present study the only assumption about the flux is that it is an entirely function of the density.