Viscous solutions of 1D conservation laws converge to the inviscid preshock at sharp rate nu^{1/4} in L∞, with Hölder thresholds 1/3 for the shocking and 2/3 for the nonshocking component, and a universal viscous Burgers profile near shock formation.
Crime pays; homogenized wave equations for long times
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Shock formation in 1D conservation laws II: Vanishing viscosity
Viscous solutions of 1D conservation laws converge to the inviscid preshock at sharp rate nu^{1/4} in L∞, with Hölder thresholds 1/3 for the shocking and 2/3 for the nonshocking component, and a universal viscous Burgers profile near shock formation.