### Initial Layers and Uniqueness of Weak Entropy Conservation Laws<

Guiqiang Chen and Michel Rascle

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 disappear. We also discuss its applications to the zero relaxation limit for hyperbolic systems of conservation laws with relaxation.

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Author(s):
Guiqiang Chen , <gqchen@math.nwu.edu>
Michel Rascle<, <rascle@math.unice.fr>
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