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

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Author(s)

  • Alberto Bressan
  • Feimin Huang
  • Yong Wang
  • Tong Yang

Detail(s)

Original languageEnglish
Pages (from-to)3537-3563
Journal / PublicationSIAM Journal on Mathematical Analysis
Volume44
Issue number5
Publication statusPublished - 2012
Externally publishedYes

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|. Copyright © by SIAM.

Research Area(s)

  • Bounded variation estimates, Convergence rates, Genuine nonlinearity, Lyapunov functionals, Riemann solution, Strictly hyperbolic, Vanishing viscosity

Citation Format(s)

On the convergence rate of vanishing viscosity approximations for nonlinear hyperbolic systems. / Bressan, Alberto; Huang, Feimin; Wang, Yong et al.
In: SIAM Journal on Mathematical Analysis, Vol. 44, No. 5, 2012, p. 3537-3563.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review