Multiple highly oscillatory shock waves

Article type: Research Article

Authors: Peng, Yahong^; | Wang, Ya-Guang

Affiliations: Department of Applied Mathematics, Donghua University, Shanghai 200051, P. R. China | Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, P. R. China

Note: [] Corresponding author. E-mail: pengyahong@dhu.edu.cn.

Abstract: This paper is devoted to the rigorous theory of nonlinear geometric optics for multiple shocks to a general N×N conservation law in one space variable. For the problem of multiple weak shocks perturbed by small amplitude, high-frequency oscillatory waves, we obtain that the leading profiles of oscillatory shocks are solution to an integro-differential system with free boundaries, the leading terms of shock fronts don't oscillate, and oscillations only appear in the leading terms shock speeds.

Keywords: nonlinear geometric optics, conservation laws, shock waves

DOI: 10.3233/ASY-2008-0864

Journal: Asymptotic Analysis, vol. 57, no. 3-4, pp. 143-198, 2008