SHARPER TOTAL VARIATION BOUNDS FOR THE P-SYSTEM OF FLUID DYNAMICS

Abstract

For the p-system of fluid dynamics and under the assumption that the initial data have small oscillation but not necessarily small total variation, we reproduce the so-called Glimm–Lax estimates with greater accuracy. Our approach recovers the results known for smooth flux functions, and is based on the theory of generalized characteristics and Dafermos' technique of polygonal approximations.