## 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) |
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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 |

## All Science Journal Classification (ASJC) codes

- Analysis
- Computational Mathematics
- Applied Mathematics