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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Stability of small amplitude boundary layers for mixed hyperbolic-parabolic systems


Author: F. Rousset
Journal: Trans. Amer. Math. Soc. 355 (2003), 2991-3008
MSC (2000): Primary 35K50, 35L50, 35L65, 76H20
Published electronically: March 17, 2003
MathSciNet review: 1975409
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Abstract: We consider an initial boundary value problem for a symmetrizable mixed hyperbolic-parabolic system of conservation laws with a small viscosity $\varepsilon$, $u^\varepsilon_t+F(u^\varepsilon)_x =\varepsilon(B(u^\varepsilon) u^\varepsilon_x )_x .$ When the boundary is noncharacteristic for both the viscous and the inviscid system, and the boundary condition dissipative, we show that $u^\varepsilon$ converges to a solution of the inviscid system before the formation of shocks if the amplitude of the boundary layer is sufficiently small. This generalizes previous results obtained for $B$ invertible and the linear study of Serre and Zumbrun obtained for a pure Dirichlet's boundary condition.


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Additional Information

F. Rousset
Affiliation: ENS Lyon, UMPA (UMR 5669 CNRS), 46, allée d’Italie, 69364 Lyon Cedex 07, France
Address at time of publication: Laboratoire Dieudonné, Université de Nice-Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 02, France
Email: frousset@umpa.ens-lyon.fr, frousset@math.unice.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03279-3
PII: S 0002-9947(03)03279-3
Received by editor(s): January 30, 2002
Received by editor(s) in revised form: December 13, 2002
Published electronically: March 17, 2003
Article copyright: © Copyright 2003 American Mathematical Society