Couches limites semilinéaires
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 15 (2006) no. 2, p. 323-380

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.

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.
@article{AFST_2006_6_15_2_323_0,
     author = {Sueur, Franck},
     title = {Couches limites semilin\'eaires},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {6e s{\'e}rie, 15},
     number = {2},
     year = {2006},
     pages = {323-380},
     doi = {10.5802/afst.1124},
     mrnumber = {2244220},
     zbl = {pre05176314},
     language = {fr},
     url = {http://www.numdam.org/item/AFST_2006_6_15_2_323_0}
}
Sueur, Franck. Couches limites semilinéaires. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 15 (2006) no. 2, pp. 323-380. doi : 10.5802/afst.1124. http://www.numdam.org/item/AFST_2006_6_15_2_323_0/

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