Uniqueness of weak solutions to systems of conservation laws

Alberto Bressan; Philippe LeFloch

doi:10.1007/s002050050068

Uniqueness of weak solutions to systems of conservation laws

Alberto Bressan, Philippe LeFloch

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

76 Scopus citations

Abstract

Consider a strictly hyperbolic n × n system of conservation laws in one space dimension: u_t + F(u)_x = 0, (*) Relying on the existence of the Standard Riemann Semigroup generated by (*), we establish the uniqueness of entropy-admissible weak solutions to the Cauchy problem, under a mild assumption on the variation of u along space-like segments.

Original language	English (US)
Pages (from-to)	301-317
Number of pages	17
Journal	Archive for Rational Mechanics and Analysis
Volume	140
Issue number	4
DOIs	https://doi.org/10.1007/s002050050068
State	Published - Dec 16 1997

All Science Journal Classification (ASJC) codes

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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title = "Uniqueness of weak solutions to systems of conservation laws",

abstract = "Consider a strictly hyperbolic n × n system of conservation laws in one space dimension: ut + F(u)x = 0, (*) Relying on the existence of the Standard Riemann Semigroup generated by (*), we establish the uniqueness of entropy-admissible weak solutions to the Cauchy problem, under a mild assumption on the variation of u along space-like segments.",

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N2 - Consider a strictly hyperbolic n × n system of conservation laws in one space dimension: ut + F(u)x = 0, (*) Relying on the existence of the Standard Riemann Semigroup generated by (*), we establish the uniqueness of entropy-admissible weak solutions to the Cauchy problem, under a mild assumption on the variation of u along space-like segments.

AB - Consider a strictly hyperbolic n × n system of conservation laws in one space dimension: ut + F(u)x = 0, (*) Relying on the existence of the Standard Riemann Semigroup generated by (*), we establish the uniqueness of entropy-admissible weak solutions to the Cauchy problem, under a mild assumption on the variation of u along space-like segments.

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Uniqueness of weak solutions to systems of conservation laws

Abstract

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