Liu, Tai-Ping Pointwise convergence to shock waves for viscous conservation laws. (English) Zbl 0902.35069 Commun. Pure Appl. Math. 50, No. 11, 1113-1182 (1997). The goal of the present paper is to study the behaviour of the perturbations of shock waves for nonlinear viscous conservation laws. The author uses a new pointwise approach, which consists of a time-asymptotic expansion, construction of approximate Green functions, and analysis of nonlinear wave interactions corresponding to different characteristic families. As an immediate consequence, the pointwise estimates yield optimal \(L^p\)-convergence of the perturbation to the shock and diffusion waves, \(1 \leq p \leq \infty\). This new approach of obtaining pointwise estimates based on Green functions for the linearized systems and the analysis of nonlinear wave interactions can be also applied to stability analysis of nonclassical shocks and various types of waves. Reviewer: Mária Lukáčová (Brno) Cited in 1 ReviewCited in 79 Documents MSC: 35L65 Hyperbolic conservation laws 76L05 Shock waves and blast waves in fluid mechanics 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 35L67 Shocks and singularities for hyperbolic equations Keywords:nonlinear viscous conservation laws; nonlinear wave interactions; Green functions PDFBibTeX XMLCite \textit{T.-P. Liu}, Commun. Pure Appl. Math. 50, No. 11, 1113--1182 (1997; Zbl 0902.35069) Full Text: DOI