### Abstract

Consider the Cauchy problem for a strictly hyperbolic 2×2 system of conservation laws in one space dimension: {ie1-01} assuming that each characteristic field is either linearly degenerate or genuinely nonlinear. This paper develops a new algorithm, based on wave-front tracking, which yields a Cauchy sequence of approximate solutions, converging to a unique limit depending continuously on the initial data. The solutions that we obtain constitute a semigroup S, defined on a set {ie1-02} of integrable functions with small total variation. For some Lipschitz constant L, we have the estimate {ie1-03}

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

Pages (from-to) | 1-75 |

Number of pages | 75 |

Journal | Archive for Rational Mechanics and Analysis |

Volume | 133 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1995 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering

### Cite this

*Archive for Rational Mechanics and Analysis*,

*133*(1), 1-75. https://doi.org/10.1007/BF00375350

}

*Archive for Rational Mechanics and Analysis*, vol. 133, no. 1, pp. 1-75. https://doi.org/10.1007/BF00375350

**The semigroup generated by 2 × 2 conservation laws.** / Bressan, Alberto; Colombo, Rinaldo M.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The semigroup generated by 2 × 2 conservation laws

AU - Bressan, Alberto

AU - Colombo, Rinaldo M.

PY - 1995/3

Y1 - 1995/3

N2 - Consider the Cauchy problem for a strictly hyperbolic 2×2 system of conservation laws in one space dimension: {ie1-01} assuming that each characteristic field is either linearly degenerate or genuinely nonlinear. This paper develops a new algorithm, based on wave-front tracking, which yields a Cauchy sequence of approximate solutions, converging to a unique limit depending continuously on the initial data. The solutions that we obtain constitute a semigroup S, defined on a set {ie1-02} of integrable functions with small total variation. For some Lipschitz constant L, we have the estimate {ie1-03}

AB - Consider the Cauchy problem for a strictly hyperbolic 2×2 system of conservation laws in one space dimension: {ie1-01} assuming that each characteristic field is either linearly degenerate or genuinely nonlinear. This paper develops a new algorithm, based on wave-front tracking, which yields a Cauchy sequence of approximate solutions, converging to a unique limit depending continuously on the initial data. The solutions that we obtain constitute a semigroup S, defined on a set {ie1-02} of integrable functions with small total variation. For some Lipschitz constant L, we have the estimate {ie1-03}

UR - http://www.scopus.com/inward/record.url?scp=34247463858&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34247463858&partnerID=8YFLogxK

U2 - 10.1007/BF00375350

DO - 10.1007/BF00375350

M3 - Article

AN - SCOPUS:34247463858

VL - 133

SP - 1

EP - 75

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

SN - 0003-9527

IS - 1

ER -