In this paper we investigate the nonlinear geometric optics of a stable shock wave perturbed by high frequency oscillations for quasilinear hyperbolic conservation laws in one space variable. We obtain the existence of the oscillatory shock wave and its leading profiles, which are solutions to a boundary value problem of integro.differential systems. Furthermore, the asymptotic properties of the oscillatory shock wave as well as the shock front are justified.
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Ya-Guang Wang, Nonlinear Geometric Optics for Shock Waves Part II: System Case. Z. Anal. Anwend. 16 (1997), no. 4, pp. 857–918DOI 10.4171/ZAA/796