Stabilité L 1 d’ondes progressives de lois de conservation scalaires
Serre, Denis1
1 UMPA, UMR # 5669 CNRS-ENS Lyon, Ecole Normale Supérieure de Lyon, 46, allée d’Italie, F-69364 Lyon cedex 07
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1998-1999), Exposé no. 8, 11 p.

A powerfull method has been developped in [2] for the study of L 1 -stability of travelling waves in conservation laws or more generally in equations which display L 1 -contractivity, maximum principle and mass conservation. We recall shortly the general procedure. We also show that it partly applies to the waves of a model of radiating gas. These waves have first been studied by Kawashima and Nishibata [5,6] in a different framework. Therefore, shock fronts for this model are stable under mild perturbations.

Serre, Denis 1

1 UMPA, UMR # 5669 CNRS-ENS Lyon, Ecole Normale Supérieure de Lyon, 46, allée d’Italie, F-69364 Lyon cedex 07 
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     title = {Stabilit\'e $L^1$ d{\textquoteright}ondes progressives de lois de conservation scalaires},
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     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
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Serre, Denis. Stabilité $L^1$ d’ondes progressives de lois de conservation scalaires. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1998-1999), Exposé no. 8, 11 p. http://archive.numdam.org/item/SEDP_1998-1999____A8_0/

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[3] H. Freistühler, D. Serre. The L 1 -stability of boundary layers for scalar viscous conservation laws. Preprint (1998). | MR | Zbl

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[7] C. Mascia, R. Natalini. L 1 nonlinear stability of travelling waves for a hyperbolic system with relaxation. J. Diff. Equations, 132 (1996), pp 275-292. | MR | Zbl

[8] D. Serre. L 1 -decay and the stability of shock profiles. Proceedings, Prague 1998. A paraî tre. | Zbl

[9] D. Serre. Stabilité des ondes de choc de viscosité qui peuvent être caractéristiques. Prepublication (1994).

[10] D. Serre. Systèmes de lois de conservation, I. Diderot arts & Sci. (1996). Paris. | MR