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\(L^1\)-stability of travelling waves in scalar conservation laws. (Stabilité \(L^1\) d’ondes progressives de lois de conservation scalaires.) (French) Zbl 1063.35520

Summary: A powerful method has been developed in [H. Freistühler and 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 S. Kawashima and 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:

35L65 Hyperbolic conservation laws
35B35 Stability in context of PDEs
35L67 Shocks and singularities for hyperbolic equations
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