Asymptotic Decay toward the Rarefaction Waves of Solutions for Viscous Conservation Laws in a One-Dimensional Half Space

Source abstract

This paper is concerned with convergence rates toward the rarefaction waves of the solutions for scalar viscous conservation laws in a half space. We show that the convergence rate is (1+t) -1/4 log (2+t) in L 2 -norm if the initial perturbation from the corresponding rarefaction waves is located in $H^1 \cap L^1$. This rate is equal to the well-known rate obtained for viscous conservation laws in the whole space. The proof is given by the combination of the standard L 2 -energy method and L 1 -estimate.