## Initial Layers and Uniqueness of Weak Entropy Solutions to
Hyperbolic Conservation Laws

#### Author: Gui-Qiang Chen and Michel Rascle

#### Title: Initial Layers and Uniqueness of Weak Entropy Solutions to
Hyperbolic Conservation Laws

**Abstract**

We consider initial layers and uniqueness of weak entropy solutions
to hyperbolic conservation laws through the scalar case.
The entropy solutions we address assume their initial data {\it only}
in the sense of weak-star in $L^\infty$ as $t\to 0_+$ and satisfy the
entropy inequality in the sense of distributions for $t>0$.
We prove that, if the flux function has weakly genuine nonlinearity,
then the entropy solutions are always unique and the initial layers
do not appear. We also discuss its applications to the zero relaxation
limit for hyperbolic systems of conservation laws with relaxation.

This article has appeared in:

*Archive for Rational Mechanics and Analysis* **vol 153**,
pages 205-220 (2000)

This paper is available in the following formats:

A closely related paper is Change me.

**Author Address**
Department of Mathematics
Northwestern University
Evanston, IL 60208-2730
gqchen@math.nwu.edu