Abstract
We investigate how chaos propagates in the solution of Burgers equation ∂ t u+u∂ x u=0 with initial condition u(ċ,0) distributed as a white noise on \(\mathbb{R}^ + \) and 0 on \(\mathbb{R}^ - \). We describe the evolution of the shock front that travels to the left. Asymptotics are given for both large and small time t.
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Giraud, C. On a Shock Front in Burgers Turbulence. Journal of Statistical Physics 111, 387–402 (2003). https://doi.org/10.1023/A:1022221511458
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DOI: https://doi.org/10.1023/A:1022221511458