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Zbl 1063.35520
Serre, Denis
$L^1$-stability of travelling waves in scalar conservation laws. (Stabilité $L^1$ d'ondes progressives de lois de conservation scalaires.) (French)
[J] Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math., Palaiseau 1998-1999, Exp. No. VIII, 13 p. (1999).

Summary: A powerful method has been developed in [{\it H. Freistühler} and {\it D. Serre}, Commun. Pure Appl. Math. 51, No. 3, 291--301 (1998; Zbl 0907.76046)] 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 {\it S. Kawashima} and {\it S. Nishibata} [SIAM J. Math. Anal. 30, No. 1, 95--117 (1999; Zbl 0924.35082); Sci. Bull. Josai Univ. Spec. Iss., No. 5, 119--130 (1998; Zbl 0915.76074)] in a different framework. Therefore, shock fronts for this model are stable under mild perturbations.

MSC 2000:: *35L65 Conservation laws
35B35 Stability of solutions of PDE
35L67 Shocks, etc.

Keywords: radiating gas; shock fronts

Citations: Zbl 0907.76046; Zbl 0924.35082; Zbl 0915.76074

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