A uniqueness condition for hyperbolic systems of conservation laws

Alberto Bressan; Marta Lewicka

doi:10.3934/dcds.2000.6.673

A uniqueness condition for hyperbolic systems of conservation laws

Alberto Bressan, Marta Lewicka

Research output: Contribution to journal › Article › peer-review

31 Scopus citations

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
DOIs	https://doi.org/10.3934/dcds.2000.6.673
State	Published - Jul 2000

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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author = "Alberto Bressan and Marta Lewicka",

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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.

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A uniqueness condition for hyperbolic systems of conservation laws

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