On the convergence rate of vanishing viscosity approximations

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)1075-1109
Journal / PublicationCommunications on Pure and Applied Mathematics
Issue number8
Publication statusPublished - Aug 2004


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. © 2004 Wiley Periodicals, Inc.