Viscous Limits for strong shocks of one-dimensional systems of conservation laws
Rousset, Frédéric
Journées équations aux dérivées partielles, (2002), p. 1-11 / Harvested from Numdam
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On considère un système hyperbolique de lois de conservation monodimensionnel u t +f(u) x =0, et une solution continue par morceaux avec un seul choc de ce système. En supposant qu’en tout point de discontinuité, il existe un profil visqueux linéairement stable, on montre qu’il existe une solution du système avec viscosité u t +f(u) x =ϵu xx qui tend vers la solution discontinue dans L ∞ ([0,T]L 1 ) lorsque la viscosité tend vers zéro.

We consider a piecewise smooth solution of a one-dimensional hyperbolic system of conservation laws with a single noncharacteristic Lax shock. We show that it is a zero dissipation limit assuming that there exist linearly stable viscous profiles associated with the discontinuities. In particular, following the approach of Grenier and Rousset (2001), we replace the smallness condition obtained by energy methods in Goodman and Xin (1992) by a weaker spectral assumption.

Publié le : 2002-01-01
DOI : https://doi.org/10.5802/jedp.614 
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     author = {Rousset, Fr\'ed\'eric},
     title = {Viscous Limits for strong shocks of one-dimensional systems of conservation laws},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {2002},
     pages = {1-11},
     doi = {10.5802/jedp.614},
     mrnumber = {1968212},
     language = {en},
     url = {http://dml.mathdoc.fr/item/JEDP_2002____A16_0}
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Rousset, Frédéric. Viscous Limits for strong shocks of one-dimensional systems of conservation laws. Journées équations aux dérivées partielles,  (2002), pp. 1-11. doi : 10.5802/jedp.614. http://gdmltest.u-ga.fr/item/JEDP_2002____A16_0/

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