In this talk we will present the works of S. Bianchini and A. Bressan on the Cauchy problem for viscous perturbations of one-dimensional strictly hyperbolic systems . They have shown global existence (), uniqueness and stability and they have justified the limit when goes to zero for initial data with small total variation. Their analysis also shows that the solutions of the hyperbolic system obtained by this method coincide with the solutions obtained by other types of approximations.
Le but de l’exposé est de présenter les résultats obtenus par S. Bianchini et A. Bressan sur le problème de Cauchy pour des perturbations visqueuses de systèmes strictement hyperboliques en une dimension d’espace. Ils ont en particulier montré l’existence globale (), l’unicité et la stabilité des solutions et justifié la convergence quand tend vers zéro pour des données initiales à petite variation totale. Leur analyse montre aussi que les solutions du système hyperbolique ainsi obtenues coïncident avec les solutions provenant d’autres types d’approximations.
Mot clés : systèmes hyperboliques, méthode de viscosité
Keywords: hyperbolic systems, vanishing viscosity method
@incollection{SB_2002-2003__45__231_0, author = {Rousset, Fr\'ed\'eric}, title = {Syst\`emes hyperboliques et viscosit\'e \'evanescente}, booktitle = {S\'eminaire Bourbaki : volume 2002/2003, expos\'es 909-923}, series = {Ast\'erisque}, note = {talk:918}, pages = {231--250}, publisher = {Association des amis de Nicolas Bourbaki, Soci\'et\'e math\'ematique de France}, address = {Paris}, number = {294}, year = {2004}, mrnumber = {2111646}, zbl = {1215.35104}, language = {fr}, url = {http://archive.numdam.org/item/SB_2002-2003__45__231_0/} }
TY - CHAP AU - Rousset, Frédéric TI - Systèmes hyperboliques et viscosité évanescente BT - Séminaire Bourbaki : volume 2002/2003, exposés 909-923 AU - Collectif T3 - Astérisque N1 - talk:918 PY - 2004 SP - 231 EP - 250 IS - 294 PB - Association des amis de Nicolas Bourbaki, Société mathématique de France PP - Paris UR - http://archive.numdam.org/item/SB_2002-2003__45__231_0/ LA - fr ID - SB_2002-2003__45__231_0 ER -
%0 Book Section %A Rousset, Frédéric %T Systèmes hyperboliques et viscosité évanescente %B Séminaire Bourbaki : volume 2002/2003, exposés 909-923 %A Collectif %S Astérisque %Z talk:918 %D 2004 %P 231-250 %N 294 %I Association des amis de Nicolas Bourbaki, Société mathématique de France %C Paris %U http://archive.numdam.org/item/SB_2002-2003__45__231_0/ %G fr %F SB_2002-2003__45__231_0
Rousset, Frédéric. Systèmes hyperboliques et viscosité évanescente, in Séminaire Bourbaki : volume 2002/2003, exposés 909-923, Astérisque, no. 294 (2004), Talk no. 918, pp. 231-250. http://archive.numdam.org/item/SB_2002-2003__45__231_0/
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