H^-1 Compactness Of η（u^ε）_t+q（u^ε）_x For Some Hyperbolic Systems

This paper describes the H-1 Compactness of η(uε)t+q(uε)x,using of compen-sation compactness theory, combined with a few classic example gives a detailed proof.The first chapter is the introduction part,outlines the hyperbolic conservation laws and the type of mainly studied in this paper.The second chapter to the fifth chapter introduces Sobolev embedding theo-rem,appling compensation compactness theory to prove H’1 compactness of the special systems of quadratic fulx, isentropic gas dynamics and others, and propose div-curl lemma.The sixth chapter give a short proof of a compactness framework of the ap-proximation solutions(pE(ρε,wiε),.