Global structure instability of Riemann solutions of quasilinear hyperbolic systems of conservation laws: Rarefaction waves

摘要

This work is a continuation of our previous work (Kong, J. Differential Equations 188 (2003) 242-271) "Global structure stability of Riemann solutions of quasilinear hyperbolic systems of conservation laws: shocks and contact discontinuities". In the present paper we prove the global structure instability of the Lax's Riemann solution u = U(x/t), containing rarefaction waves, of general n x n quasilinear hyperbolic system of conservation laws. Combining the results in (Kong, 2003), we prove that the Lax's Riernarm solution of general n x n quasilinear hyperbolic system of conservation laws is globally structurally stable if and only if it contains only non-degenerate shocks and contact discontinuities, but no rarefaction waves and other weak discontinuities. (c) 2005 Elsevier Inc. All rights reserved.