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A mixed type system of three equations modelling reacting flows

Authors: Yun-guang Lu and Christian Klingenberg
Journal: Proc. Amer. Math. Soc. 131 (2003), 3511-3516
MSC (2000): Primary 35L65; Secondary 35M10
Published electronically: April 1, 2003
MathSciNet review: 1991763
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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{displaymath}u_t +{f(u)}_x = \alpha g(u) \quad . \end{displaymath}

In one approach this is proven under some suitable stability condition; in the other approach, one adds artificial viscosity to the system

\begin{displaymath}u_t +{f(u)}_x = \alpha g(u) + \epsilon u_{xx} \end{displaymath}

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.

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Additional 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

Christian Klingenberg
Affiliation: Applied Mathematics, Würzburg University, Am Hubland, Würzburg 97074, Germany

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
Article copyright: © Copyright 2003 American Mathematical Society