Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 61, No. 4, pp. 479-499 (2004)

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On the validity of Chapman--Enskog expansions for shock waves with small strength

N. Bedjaoui, C. Klingenberg and P.G. LeFloch

INSSET, Université de Picardie,
48 rue Raspail, 02109 Saint-Quentin -- FRANCE
E-mail: bedjaoui@cmap.polytechnique.fr
Applied Mathematics Department, Würzburg University,
Am Hubland, 97074 Würzburg -- GERMANY
E-mail: klingen@mathematik.uni-wuerzburg.de
Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientifique, U.M.R. 7598,
Université Pierre et Marie Curie, 75252 Paris -- FRANCE
E-mail: lefloch@ann.jussieu.fr

Abstract: We justify a Chapman--Enskog expansion for discontinuous solutions of hyperbolic conservation laws containing shock waves with {\sl small} strength. Precisely, we establish pointwise uniform estimates for the difference between the traveling waves of a relaxation model and the traveling waves of the corresponding diffusive equations determined by a Chapman--Enskog expansion procedure to first- or second-order.

Keywords: conservation law; hyperbolic; shock wave; traveling wave; relaxation; diffusion; Chapman--Enskog expansion.

Classification (MSC2000): 35L65, 76N10.

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Electronic version published on: 7 Mar 2008.

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