Multiple highly oscillatory shock waves

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.