On the convergence rate of vanishing viscosity approximations

Alberto Bressan, Tong Yang

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

Given a strictly hyperbolic, genuinely nonlinear system of conservation laws, we prove the a priori bound ||u(t, ·) - uε(t, ·)||L1 = script O sign (1)(1 + t) · √ε|ln ε| on the distance between an exact BV solution M and a viscous approximation uε, letting the viscosity coefficient ε → 0. In the proof, starting from u we construct an approximation of the viscous solution uε by taking a mollification u *φ √ε and inserting viscous shock profiles at the locations of finitely many large shocks for each fixed ε. Error estimates are then obtained by introducing new Lyapunov functionals that control interactions of shock waves in the same family and also interactions of waves in different families.

Original languageEnglish (US)
Pages (from-to)1075-1109
Number of pages35
JournalCommunications on Pure and Applied Mathematics
Volume57
Issue number8
DOIs
StatePublished - Aug 1 2004

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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