Convergence rates to viscous shock profile for general scalar viscous conservation laws with large initial disturbance

Abstract

This paper is concerned with the convergence rates to viscous shock profile for general scalar viscous conservation laws. Compared with former results in this direction, the main novelty in this paper lies in the fact that the initial disturbance can be chosen arbitrarily large. This answers positively an open problem proposed by A. Matsumura in [12] and K. Nishihara in [16]. Our analysis is based on the $L^1\text{-}$ stability results obtained by H. Freistiihler and D. Serre in [1].