On the convergence of viscous approximations after shock interactions

Pages: 29 - 48, Volume 23, Issue 1/2, January/February 2009

doi:10.3934/dcds.2009.23.29       Abstract        Full Text (221.8K)       Related Articles

Alberto Bressan - Penn State University Mathematics Dept., University Park, State College, PA 16802, United States (email)
Carlotta Donadello - S.I.S.S.A.-I.S.A.S., Via Beirut 4, Trieste 34014, Italy (email)

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.

Keywords:  scalar conservation laws with viscosity, viscous shock profiles, singular perturbation expansion
Mathematics Subject Classification:  Primary: 35L65, 35B25

Received: July 2007;      Revised: December 2007;      Published: September 2008.