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

Alberto Bressan, Feimin Huang, Yong Wang, Tong Yang

Research output: Contribution to journalArticle

5 Citations (Scopus)

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

Fingerprint

Viscosity Approximation
Nonlinear Hyperbolic Systems
Vanishing Viscosity
Rate of Convergence
Linearly
Viscosity
Total Variation
Hyperbolic Systems
Straight Line
Estimate
Strictly
Exact Solution
Curve
Approximation

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

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On the convergence rate of vanishing viscosity approximations for nonlinear hyperbolic systems. / Bressan, Alberto; Huang, Feimin; Wang, Yong; Yang, Tong.

In: SIAM Journal on Mathematical Analysis, Vol. 44, No. 5, 09.11.2012, p. 3537-3563.

Research output: Contribution to journalArticle

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