On the convergence of viscous approximations after shock interactions

Alberto Bressan; Carlotta Donadello

doi:10.3934/dcds.2009.23.29

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2009, Volume 23, Issue 1&2: 29-48. Doi: 10.3934/dcds.2009.23.29

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On the convergence of viscous approximations after shock interactions

Alberto Bressan^1, and
Carlotta Donadello^2,

1.
Penn State University Mathematics Dept., University Park, State College, PA 16802
2.
S.I.S.S.A.-I.S.A.S., Via Beirut 4, Trieste 34014

Received: July 2007

Revised: December 2007

Published: May 2009

Abstract / Introduction Related Papers Cited by

Abstract

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

Keywords:

scalar conservation laws with viscosity,
viscous shock profiles,
singular perturbation expansion.

Mathematics Subject Classification: Primary: 35L65, 35B25.

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