Burgers’ Equation with Vanishing Hyper-viscosity∗

We prove that bounded solutions of the vanishing hyper-viscosity equation, ut + f(u)x + (−1)sε∂2s x u = 0 converge to the entropy solution of the corresponding convex conservation law ut+f(u)x = 0, f ′′ > 0. The hyper-viscosity case, s > 1, lacks the monotonicity which underlines the Krushkov BV theory in the viscous case s = 1. Instead we show how to adapt… (More)