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January & February  2009, 23(1&2): 29-48. doi: 10.3934/dcds.2009.23.29

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, United States
2. 

S.I.S.S.A.-I.S.A.S., Via Beirut 4, Trieste 34014, Italy

Received  July 2007 Revised  December 2007 Published  September 2008

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.
Keywords: scalar conservation laws with viscosity, viscous shock profiles, singular perturbation expansion.
Mathematics Subject Classification: Primary: 35L65, 35B25.
Citation: Alberto Bressan, Carlotta Donadello. On the convergence of viscous approximations after shock interactions. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 29-48. doi: 10.3934/dcds.2009.23.29
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