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Error estimates for oscillatory solutions to hyperbolic systems of conservation laws. (English) Zbl 0818.35061

Summary: This paper deals with oscillatory solutions of one dimensional systems of conservation laws endowed with one linearly degenerate characteristic field. Recently, E. Weinan [Commun. Partial Differ. Equations 17, No. 3/4, 347-370 (1992; Zbl 0760.35007)] and D. Serre [Semin. Equ. Deriv. Partielles, Ec. Polytech., 1990-1991, No. 20, 18 p. (1991; Zbl 0755.35071)] derived a system of homogenized equations, by using a multiple scale analysis. Our goal is to prove rigorous error estimates in order to justify the validity of these equations, at least when initial data are smooth.

MSC:

35L65 Hyperbolic conservation laws
35A35 Theoretical approximation in context of PDEs
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
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