We are interested in some multidimensional semilinear symmetric hyperbolic systems. It is well known that these systems have some discontinuous solutions which are regular outside of a smooth hypersurface characteristic of constant multiplicity. We suppose that such a solution is given and we show that is the limit, when , of solutions of the system perturbated by a viscosity of size . The key tools of the proof are a parabolic boundary problem and boundary layers expansions. We also consider weaker singularities as derivatives jumps.
On s’intéresse à des systèmes symétriques hyperboliques multidimensionnels en présence d’une semilinéarité. Il est bien connu que ces systèmes admettent des solutions discontinues, régulières de part et d’autre d’une hypersurface lisse caractéristique de multiplicité constante. Une telle solution étant donnée, on montre que est limite quand de solutions du système perturbé par une viscosité de taille . La preuve utilise un problème mixte parabolique et des développements de couches limites. On s’intéresse aussi à des singularités plus faibles comme des sauts de dérivées.
Keywords: approche visqueuse, couches limites, solutions discontinues
@article{AIF_2006__56_1_183_0, author = {Sueur, Franck}, title = {Approche visqueuse de solutions discontinues de syst\`emes hyperboliques semilin\'eaires}, journal = {Annales de l'Institut Fourier}, pages = {183--245}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {56}, number = {1}, year = {2006}, doi = {10.5802/aif.2177}, zbl = {1094.35024}, mrnumber = {2228685}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/aif.2177/} }
TY - JOUR AU - Sueur, Franck TI - Approche visqueuse de solutions discontinues de systèmes hyperboliques semilinéaires JO - Annales de l'Institut Fourier PY - 2006 SP - 183 EP - 245 VL - 56 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2177/ DO - 10.5802/aif.2177 LA - fr ID - AIF_2006__56_1_183_0 ER -
%0 Journal Article %A Sueur, Franck %T Approche visqueuse de solutions discontinues de systèmes hyperboliques semilinéaires %J Annales de l'Institut Fourier %D 2006 %P 183-245 %V 56 %N 1 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2177/ %R 10.5802/aif.2177 %G fr %F AIF_2006__56_1_183_0
Sueur, Franck. Approche visqueuse de solutions discontinues de systèmes hyperboliques semilinéaires. Annales de l'Institut Fourier, Volume 56 (2006) no. 1, pp. 183-245. doi : 10.5802/aif.2177. http://www.numdam.org/articles/10.5802/aif.2177/
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