On the formation of scalar viscous shocks problem
by Alberto Bressan, Carlotta Donadello
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 1, No. 1, 2007

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.

Online publication date: Wed, 23-May-2007

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