### Analysis of a scalar conservation law with a flux function with discontinuous coefficients

Florence Bachmann

#### Abstract

We study here a model of a conservation law with a flux function with discontinuous coefficients, namely the equation $u_t + (k(x)g(u)+f(u))_x=0$. We prove the existence and the uniqueness of an entropy solution in $L^{\infty}(\mathbb R_+ \times \mathbb R)$ for $u_0$, the initial condition, in $L^{\infty}(\mathbb R)$. We provide some physical background for the study of this equation. In particular, $g$ is assumed to be neither convex nor concave and $k$ is a discontinuous function.

#### Article information

Source
Adv. Differential Equations Volume 9, Number 11-12 (2004), 1317-1338.

Dates
First available in Project Euclid: 18 December 2012

Mathematical Reviews number (MathSciNet)
MR2099558

Zentralblatt MATH identifier
1102.35063

Subjects
Primary: 35L65: Conservation laws
Secondary: 35B25: Singular perturbations

#### Citation

Bachmann, Florence. Analysis of a scalar conservation law with a flux function with discontinuous coefficients. Adv. Differential Equations 9 (2004), no. 11-12, 1317--1338.https://projecteuclid.org/euclid.ade/1355867904