Abstract
Assuming that each characteristic field is either genuinely nonlinear or linearly degenerate in the sense of Lax, we prove the global existence and uniqueness of piecewise C1 solution containing n small amplitude waves (shocks corresponding to genuinely nonlinear fields and contact discontinuities corresponding to linearly degenerate fields) for the generalized Riemann problem associated with quasilinear hyperbolic systems of conservation laws with small, decaying, piecewise C1 initial data. The solution possesses a global structure similar to that of the similarity solution to the corresponding Riemann problem.
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