L2-type contraction for shocks of scalar viscous conservation laws with strictly convex flux

L2-contraction for Shock Waves of Scalar Viscous Conservation Laws

We consider the L-contraction up to a shift for viscous shocks of scalar viscous conservation laws with strictly convex fluxes in one space dimension. In the case of a flux which is a small perturbation of the quadratic burgers flux, we show that any viscous shock induces a contraction in L, up to a shift. That is, the L norm of the difference of any solution of the viscous conservation law, wi...

L2-contraction of Large Planar Shock Waves for Multi-dimensional Scalar Viscous Conservation Laws

We consider a L-contraction (a L-type stability) of large viscous shock waves for the multi-dimensional scalar viscous conservation laws, up to a suitable shift. The shift function, depending both on the time and space variables, solves a viscous HamiltonJacobi equation with source terms. We consider a suitably small L-perturbation around a viscous planar shock wave with arbitrarily large stren...

Viscous Conservation Laws, Part I: Scalar Laws

Viscous conservation laws are the basic models for the dissipative phenomena. We aim at a systematic presentation of the basic ideas for the quantitative study of the nonlinear waves for viscous conservation laws. The present paper concentrates on the scalar laws; an upcoming Part II will deal with the systems. The basic ideas for scalar viscous conservation laws originated from two sources: th...

L2 formulation of multidimensional scalar conservation laws

Decay rate for perturbations of stationary discrete shocks for convex scalar conservation laws

This paper is to study the decay rate for perturbations of stationary discrete shocks for the Lax-Friedrichs scheme approximating the scalar conservation laws by means of an elementary weighted energy method. If the summation of the initial perturbation over (−∞, j) is small and decays at the algebraic rate as |j| → ∞, then the solution approaches the stationary discrete shock profiles at the c...