Long-Time Behavior of Scalar Viscous Shock Fronts in Two Dimensions

    loading  Checking for direct PDF access through Ovid

Abstract

We prove nonlinear stability in L1 of planar shock front solutions to a viscous conservation law in two spatial dimensions and obtain an expression for the asymptotic form of small perturbations. The leading-order behavior is shown rigorously to be governed by an effective diffusion coefficient depending on forces transverse to the shock front. The proof is based on a spectral analysis of the linearized problem.

Related Topics

    loading  Loading Related Articles