### Abstract

Consider the Cauchy problem for a hyperbolic n × n system of conservation laws in one space dimension: u_{t} + f(u)_{cursive Greek chi} = 0, u(0, cursive Greek chi) = ū(cursive Greek chi). (CP) Relying on the existence of a continuous semigroup of solutions, we prove that the entropy admissible solution of (CP) is unique within the class of functions u = u(t, cursive Greek chi) which have bounded variation along a suitable family of space-like curves.

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

Pages (from-to) | 673-682 |

Number of pages | 10 |

Journal | Discrete and Continuous Dynamical Systems |

Volume | 6 |

Issue number | 3 |

State | Published - Jul 2000 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Discrete and Continuous Dynamical Systems*,

*6*(3), 673-682.

}

*Discrete and Continuous Dynamical Systems*, vol. 6, no. 3, pp. 673-682.

**A uniqueness condition for hyperbolic systems of conservation laws.** / Bressan, Alberto; Lewicka, Marta.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A uniqueness condition for hyperbolic systems of conservation laws

AU - Bressan, Alberto

AU - Lewicka, Marta

PY - 2000/7

Y1 - 2000/7

N2 - Consider the Cauchy problem for a hyperbolic n × n system of conservation laws in one space dimension: ut + f(u)cursive Greek chi = 0, u(0, cursive Greek chi) = ū(cursive Greek chi). (CP) Relying on the existence of a continuous semigroup of solutions, we prove that the entropy admissible solution of (CP) is unique within the class of functions u = u(t, cursive Greek chi) which have bounded variation along a suitable family of space-like curves.

AB - Consider the Cauchy problem for a hyperbolic n × n system of conservation laws in one space dimension: ut + f(u)cursive Greek chi = 0, u(0, cursive Greek chi) = ū(cursive Greek chi). (CP) Relying on the existence of a continuous semigroup of solutions, we prove that the entropy admissible solution of (CP) is unique within the class of functions u = u(t, cursive Greek chi) which have bounded variation along a suitable family of space-like curves.

UR - http://www.scopus.com/inward/record.url?scp=0034384317&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034384317&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0034384317

VL - 6

SP - 673

EP - 682

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

SN - 1078-0947

IS - 3

ER -