Couches limites semilinéaires

Sueur, Franck

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 15 (2006) no. 2, pp. 323-380.

On s’intéresse à des problèmes mixtes pour des systèmes symétriques hyperboliques multidimensionnels semilinéaires perturbés par une petite viscosité. La description à la limite non visqueuse recquiert des développements du type BKW mettant en évidence une couche limite caractéristique (CLC) et une couche limite non caractéristique (CLNC). Ce thème traité dans [12] est ici enrichi de trois améliorations :

• l’étude inclut des développements ayant peu de termes (comme un seul terme),
• on étudie aussi bien la propagation que le problème de Cauchy et les conditions de compatibilité des données,
• l’étude de l’interaction CLC-CLNC est approfondie.

In this article, we consider boundary problem for semilinear symmetric hyperbolic systems in several space dimensions perturbated by a small viscosity. This theme is tackled in [12] and the inviscid limit is described by WKB-like asymptotic expansions. The latter involve characteristic and non characteristic boundary layers. Here, we give three improvements :

• we consider expansions with a few terms (for example with one term),
• we also look at the initial boundary value problem and at compatibilities between initial and boundaries data,
• the interaction between the non characteristic boundary layer and the characteristic one is pushed further.

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