Burgers' Equation with Vanishing Hyper-Viscosity
Burgers' Equation with Vanishing Hyper-Viscosity
We prove that bounded solutions of the vanishing hyper-viscosity equation, ut + f (u)x + (-1) s ε∂ 2sx 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 …