On the convergence of viscous approximations after shock interactions

Alberto Bressan; Carlotta Donadello

doi:10.3934/dcds.2009.23.29

On the convergence of viscous approximations after shock interactions

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Abstract

We consider a piecewise smooth solution to a scalar conservation law, with possibly interacting shocks. We show that, after the interactions have taken place, vanishing viscosity approximations can still be represented by a regular expansion on smooth regions and by a singular perturbation expansion near the shocks, in terms of powers of the viscosity coefficient.

Original language	English (US)
Pages (from-to)	29-48
Number of pages	20
Journal	Discrete and Continuous Dynamical Systems
Volume	23
Issue number	1-2
DOIs	https://doi.org/10.3934/dcds.2009.23.29
State	Published - Jan 2009

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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abstract = "We consider a piecewise smooth solution to a scalar conservation law, with possibly interacting shocks. We show that, after the interactions have taken place, vanishing viscosity approximations can still be represented by a regular expansion on smooth regions and by a singular perturbation expansion near the shocks, in terms of powers of the viscosity coefficient.",

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On the convergence of viscous approximations after shock interactions

Abstract

All Science Journal Classification (ASJC) codes

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