### Decay of Positive Waves in Nonlinear Systems of Conservation Laws

Alberto Bressan and Rinaldo M. Colombo

Abstract: This paper is concerned with BV solutions to a system of conservation laws in one space dimension:
$$u_t+ \left[ f(u) \right]_x = 0$$
Here $t \in [0,T]$ and $f \colon \Omega \mapsto {\bf R}^n$ is smooth, with $\Omega \subseteq {\bf R}^n$. We assume that the system is strictly hyperbolic, and that each characteristic field is either linearly degenerate or genuinely nonlinear. Our aim is to derive a priori bounds on the strength of positive waves of genuinely nonlinear families, which extend the classical decay estimates of Oleinik.

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Title: Decay of Positive Waves in Nonlinear Systems of Conservation Laws
Author(s):
Alberto Bressan <bressan@sissa.it>
Rinaldo M. Colombo <rinaldo@imiucca.csi.unimi.it>
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