On the formation of scalar viscous shocks

Alberto Bressan; Carlotta Donadello

doi:10.1504/IJDSDE.2007.013740

On the formation of scalar viscous shocks

Alberto Bressan, Carlotta Donadello

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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.

Original language	English (US)
Pages (from-to)	1-11
Number of pages	11
Journal	International Journal of Dynamical Systems and Differential Equations
Volume	1
Issue number	1
DOIs	https://doi.org/10.1504/IJDSDE.2007.013740
State	Published - 2007

All Science Journal Classification (ASJC) codes

General Engineering
Discrete Mathematics and Combinatorics
Control and Optimization

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10.1504/IJDSDE.2007.013740

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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.",

author = "Alberto Bressan and Carlotta Donadello",

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AB - 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.

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JO - International Journal of Dynamical Systems and Differential Equations

JF - International Journal of Dynamical Systems and Differential Equations

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On the formation of scalar viscous shocks

Abstract

All Science Journal Classification (ASJC) codes

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