Bressan, Alberto; Donadello, Carlotta On the formation of scalar viscous shocks problem. (English) Zbl 1161.35444 Int. J. Dyn. Syst. Differ. Equ. 1, No. 1, 1-11 (2007). Consider a viscous scalar conservation law with smooth, possibly non-convex flux. Assume that the (arbitrarily large) initial data remains in a small neighborhood of given states \(u', u''\) as \(x \rightarrow \pm \infty\) with \(u'\), \(u''\) connected by a stable shockprofile. We then show that the solution eventually forms a viscous shock. The time needed for the shock to appear is the main focus of the present analysis. Cited in 1 Document MSC: 35L67 Shocks and singularities for hyperbolic equations 35L65 Hyperbolic conservation laws 35B40 Asymptotic behavior of solutions to PDEs Keywords:shock formation time; non-convex flux PDFBibTeX XMLCite \textit{A. Bressan} and \textit{C. Donadello}, Int. J. Dyn. Syst. Differ. Equ. 1, No. 1, 1--11 (2007; Zbl 1161.35444) Full Text: DOI