## A mixed type system of three equations modelling reacting flows

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- by Yun-guang Lu and Christian Klingenberg
- Proc. Amer. Math. Soc.
**131**(2003), 3511-3516 - DOI: https://doi.org/10.1090/S0002-9939-03-06958-2
- Published electronically: April 1, 2003
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## Abstract:

In this paper we contrast two approaches for proving the validity of relaxation limits $\alpha \rightarrow \infty$ of systems of balance laws \begin{equation*} u_t +{f(u)}_x = \alpha g(u) \quad . \end{equation*} In one approach this is proven under some suitable stability condition; in the other approach, one adds artificial viscosity to the system \begin{equation*} u_t +{f(u)}_x = \alpha g(u) + \epsilon u_{xx} \end{equation*} and lets $\alpha \rightarrow \infty$ and $\epsilon \rightarrow 0$ together with $M \alpha \leq \epsilon$ for a suitable large constant $M$. We illustrate the usefulness of this latter approach by proving the convergence of a relaxation limit for a system of mixed type, where a subcharacteristic condition is not available.## References

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## Bibliographic Information

**Yun-guang Lu**- Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, People’s Republic of China – and – Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia
- Email: yglu@matematicas.unal.edu.co
**Christian Klingenberg**- Affiliation: Applied Mathematics, Würzburg University, Am Hubland, Würzburg 97074, Germany
- MR Author ID: 221691
- Email: Christian.Klingenberg@iwr.uni-heidelberg.de
- Received by editor(s): November 1, 2000
- Received by editor(s) in revised form: June 6, 2002
- Published electronically: April 1, 2003
- Communicated by: Suncica Canic
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**131**(2003), 3511-3516 - MSC (2000): Primary 35L65; Secondary 35M10
- DOI: https://doi.org/10.1090/S0002-9939-03-06958-2
- MathSciNet review: 1991763