Title: On the formation of scalar viscous shocks problem

Authors: Alberto Bressan, Carlotta Donadello

Addresses: Department of Mathematics, Penn State University, University Park, Pa. 16802, USA. ' S.I.S.S.A., Via Beirut 4, Trieste 34014, Italy

Abstract: Consider a viscous scalar conservation law with smooth, possibly non-convex flux. Assume that the (arbitrarily large) initial data remains in a small neighbourhood of given states u^-, u⁺ as x → ± ∞, with u^-, u⁺ connected by a stable shock profile. 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.

Keywords: scalar conservation laws; viscosity; viscous shock profiles.

DOI: 10.1504/IJDSDE.2007.013740

International Journal of Dynamical Systems and Differential Equations, 2007 Vol.1 No.1, pp.1 - 11

Published online: 23 May 2007 *

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