Artifical and physical viscosity solutions for a hyperbolic conservation system

Abstract

In this paper, a new maximum principle is introduced to study positive lower bounds of the density both for the artificial viscosity solutions and for the physical viscosity solutions of a 'hyperbolic conservationsystem derived from the Broadwell model and the global existence of theseviscosity solutions is obtained. We give some simple numerical results fordiscontinuous initial data.

Keywords:

• Eular equations
• artificial and physical viscosity
• invariant regions and maximum principle
• existence of global solution

AMS:

• 35B05
• 35B50
• 35L65
• 74G25