# American Institute of Mathematical Sciences

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 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.
Citation: Alberto Bressan, Carlotta Donadello. On the convergence of viscous approximations after shock interactions. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 29-48. doi: 10.3934/dcds.2009.23.29
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