Multiple Highly Oscillatory Shock Waves
This note 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 solutions 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 of shock speeds
KeywordsShock Wave Shock Front Contact Discontinuity Shock Speed Goursat Problem
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