ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 35B05, 35L65, 35L67 Wang, Ya-Guang, Shanghai Jiao Tong University, P. R. China Nonlinear Geometrical Optics for Shock Waves This talk is devoted to the asymptotic analysis and rigorous justification of the nonlinear geometrical optics for shock waves of hyperbolic conservation laws in one space variable. The existence and asymptotic properties of highly oscillatory shock waves are established by studying Goursat problems of free boundaries. We obtain that the principal profiles of the oscillatory shock waves satisfy nonlinear integro-differential systems. Furthermore, it is observed that the leading terms of shock fronts don’t oscillate, and oscillations only appear in the leading terms of shock speeds.