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Zeitschrift für Analysis und ihre Anwendungen


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Volume 16, Issue 4, 1997, pp. 857–918
DOI: 10.4171/ZAA/796

Published online: 1997-12-31

Nonlinear Geometric Optics for Shock Waves Part II: System Case

Ya-Guang Wang[1]

(1) Jiao Tong University, Shanghai, China

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.

Keywords: Nonlinear geometric optics, conservation laws, shock waves

Wang Ya-Guang: Nonlinear Geometric Optics for Shock Waves Part II: System Case. Z. Anal. Anwend. 16 (1997), 857-918. doi: 10.4171/ZAA/796