Abstract:Given a strictly hyperbolic, genuinely nonlinear system of conservation laws, we prove the a priori bound $\big\|u(t,\cdot)-u^\ve(t,\cdot)\big\|_{\L^1}= \O(1)(1+t)\cdot \sqrt\ve|\ln\ve|$ on the distance between an exact BV solution $u$ and a viscous approximation $u^\ve$, letting the viscosity coefficient $\ve\to 0$. In the proof, starting from $u$ we construct an approximation of the viscous solution $u^\ve$ by taking a mollification $u*\varphi_{\strut \sqrt\ve}$ and inserting viscous shock profiles at the locations of finitely many large shocks, for each fixed $\ve$. Error estimates are then obtained by introducing new Lyapunov functionals which control shock interactions, interactions between waves of different families and by using sharp decay estimates for positive nonlinear waves.

**Paper:**- Available as PostScript (512 Kbytes) or gzipped PostScript (200 Kbytes; uncompress using gunzip).
**Author(s):**- Alberto Bressan, <bressan@sissa.it>
- Tong Yang, <matyang@cityu.edu.hk>
**Publishing information:**- To appear in Comm. Pure Appl. Math.
**Comments:****Submitted by:**- <matyang@cityu.edu.hk> June 17 2003.

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Conservation Laws Preprint Server <conservation@math.ntnu.no> 2003-10-24 14:20:03 UTC