### Abstract

In this paper we study the zero dissipation problem for a general system of conservation laws with positive viscosity. It is shown that if the solution of the problem with zero viscosity is piecewise smooth with a finite number of noninteracting shocks satisfying the entropy condition, then there exist solutions to the corresponding system with viscosity that converge to the solutions of the system without viscosity away from shock discontinuities at a rate of order ε as the viscosity coefficient ε goes to zero. The proof uses a matched asymptotic analysis and an energy estimate related to the stability theory for viscous shock profiles.

Original language | English (US) |
---|---|

Pages (from-to) | 235-265 |

Number of pages | 31 |

Journal | Archive for Rational Mechanics and Analysis |

Volume | 121 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1992 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics (miscellaneous)
- Mathematics(all)
- Mechanics of Materials
- Computational Mechanics

### Cite this

*Archive for Rational Mechanics and Analysis*,

*121*(3), 235-265. https://doi.org/10.1007/BF00410614

**Viscous limits for piecewise smooth solutions to systems of conservation laws.** / Goodman, Jonathan; Xin, Zhouping.

Research output: Contribution to journal › Article

*Archive for Rational Mechanics and Analysis*, vol. 121, no. 3, pp. 235-265. https://doi.org/10.1007/BF00410614

}

TY - JOUR

T1 - Viscous limits for piecewise smooth solutions to systems of conservation laws

AU - Goodman, Jonathan

AU - Xin, Zhouping

PY - 1992/9

Y1 - 1992/9

N2 - In this paper we study the zero dissipation problem for a general system of conservation laws with positive viscosity. It is shown that if the solution of the problem with zero viscosity is piecewise smooth with a finite number of noninteracting shocks satisfying the entropy condition, then there exist solutions to the corresponding system with viscosity that converge to the solutions of the system without viscosity away from shock discontinuities at a rate of order ε as the viscosity coefficient ε goes to zero. The proof uses a matched asymptotic analysis and an energy estimate related to the stability theory for viscous shock profiles.

AB - In this paper we study the zero dissipation problem for a general system of conservation laws with positive viscosity. It is shown that if the solution of the problem with zero viscosity is piecewise smooth with a finite number of noninteracting shocks satisfying the entropy condition, then there exist solutions to the corresponding system with viscosity that converge to the solutions of the system without viscosity away from shock discontinuities at a rate of order ε as the viscosity coefficient ε goes to zero. The proof uses a matched asymptotic analysis and an energy estimate related to the stability theory for viscous shock profiles.

UR - http://www.scopus.com/inward/record.url?scp=21144475728&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21144475728&partnerID=8YFLogxK

U2 - 10.1007/BF00410614

DO - 10.1007/BF00410614

M3 - Article

AN - SCOPUS:21144475728

VL - 121

SP - 235

EP - 265

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

SN - 0003-9527

IS - 3

ER -