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

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Bedjaoui, Nabil
Klingenberg, Christian
LeFloch, Philippe G.
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Abstract
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We justify a Chapman-Enskog expansion for discontinuous solutions of hyperbolic conservation laws containing shock waves with 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.
Comment: 18 pages
Keywords
Mathematics - Analysis of PDEs, Mathematics - Numerical Analysis, 35L65, 76N10
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