### 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 language | English (US) |
---|---|

Pages (from-to) | 3537-3563 |

Number of pages | 27 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 44 |

Issue number | 5 |

DOIs | |

State | Published - Nov 9 2012 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Computational Mathematics
- Applied Mathematics

### Cite this

*SIAM Journal on Mathematical Analysis*,

*44*(5), 3537-3563. https://doi.org/10.1137/120869249

}

*SIAM Journal on Mathematical Analysis*, vol. 44, no. 5, pp. 3537-3563. https://doi.org/10.1137/120869249

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the convergence rate of vanishing viscosity approximations for nonlinear hyperbolic systems

AU - Bressan, Alberto

AU - Huang, Feimin

AU - Wang, Yong

AU - Yang, Tong

PY - 2012/11/9

Y1 - 2012/11/9

N2 - 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|.

AB - 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|.

UR - http://www.scopus.com/inward/record.url?scp=84868346805&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84868346805&partnerID=8YFLogxK

U2 - 10.1137/120869249

DO - 10.1137/120869249

M3 - Article

AN - SCOPUS:84868346805

VL - 44

SP - 3537

EP - 3563

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 5

ER -