Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 26, pp. 1-21.
Title: On 2X2 systems of conservation laws with fluxes that
are entropies
Author: Michael Junk (Univ. Kaiserslautern, Germany)
Abstract:
In this article, we study systems of conservation laws with
two dependent and two independent variables which have the
property that the fluxes are entropies.
Several characterizations of such flux functions are presented.
It turns out, that the corresponding systems automatically
possess a large class of additional entropies, they are closely
related to a kinetic equation, and, in the case of strict
hyperbolicity, they can be decoupled into two independent Burgers'
equations. The isentropic Euler equations with zero or cubic
pressure laws are the most prominent examples of such systems,
but other examples are also presented.
Submitted August 26, 2002. Published March 13, 2003.
Math Subject Classifications: 35L65, 82C40.
Key Words: Nonlinear conservation laws; entropies; kinetic formulation