On the convergence rate of vanishing viscosity approximations for nonlinear hyperbolic systems

Alberto Bressan, Feimin Huang, Yong Wang, Tong Yang

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Abstract

In this paper we study the vanishing viscosity limit of strictly hyperbolic systems, extending the earlier result in [A. Bressan and T. Yang, Comm. Pure Appl. Math., 57 (2004), pp. 1075-1109] to systems where each characteristic field can be either genuinely nonlinear or linearly degenerate. For a given initial data with small total variation, our main estimate shows that the L1 distance between the exact solution u and a viscous approximation ue is bounded by u(t, .) - u ε(t, .)L 1 = O(1) . (1 + t)e1/4. Under the additional assumptions that the integral curves of all linearly degenerate fields are straight lines, we obtain the sharper estimate u(t, .) - u ε(t, .)L 1 = O(1)(1 + t)ε| ln ε|.

Original languageEnglish (US)
Pages (from-to)3537-3563
Number of pages27
JournalSIAM Journal on Mathematical Analysis
Volume44
Issue number5
DOIs
StatePublished - Nov 9 2012

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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