Error estimates for oscillatory solutions to hyperbolic systems of conservation laws

This paper deals with oscillatory solutions of one dimensional syterns of conservation laws endowed with one linearly degenerate characteristic field. Recently, Weinan E (cf. 3]) and D. Sene (cf. 11]) derived a system of homogenized equations, by using a multiple scale analysis. Our goal is to prove rigourous error estimates in order to justify the validity of these equations, at least when initial data are smooth.