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Convergence rates to viscous shock profile for general scalar viscous conservation laws with large initial disturbance. (English) Zbl 1039.35064

The authors study the convergence rates to viscous shock profile for general scalar viscous conservation laws. For the initial value problem under consideration the disturbance of the initial data is allowed to be large, so that the main theorem obtained in this paper substantially extends the previous results. The method in this paper is based on the \(L\) estimate introduced by H. Freistühler and D. Serre [Commun. Pure Appl. Math. 51, 291–301 (1998; Zbl 0907.76046); J. Dyn. Differ. Equations 13, 745–755 (2001; Zbl 0993.35063)].

MSC:

35L67 Shocks and singularities for hyperbolic equations
35L65 Hyperbolic conservation laws
35L45 Initial value problems for first-order hyperbolic systems
35B45 A priori estimates in context of PDEs
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