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

On the convergence of viscous approximations after shock interactions

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.
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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