Convergence of a family of perturbed conservation laws with diffusion and non-positive dispersion

Abstract

We consider a family of conservation laws with convex flux perturbed by vanishing diffusion and non-positive dispersion of the form ut+f(u)x=εuxx−δ(|uxx|n)x. Convergence of the solutions {uε,δ} to the entropy weak solution of the hyperbolic limit equation ut+f(u)x=0, for all real numbers 1≤n≤2 is proved if δ=o(ε3n−12;ε5n−12(2n−1)).