A uniqueness condition for hyperbolic systems of conservation laws

Alberto Bressan; Marta Lewicka

doi:10.3934/dcds.2000.6.673

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2000, Volume 6, Issue 3: 673-682. Doi: 10.3934/dcds.2000.6.673

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A uniqueness condition for hyperbolic systems of conservation laws

Alberto Bressan^1, and
Marta Lewicka^2,

1.
S.I.S.S.A., Via Beirut, 2-4, 34014 Trieste
2.
SISSA, via Beirut 2-4, 34014 Trieste

Received: November 30, 1999

Revised: February 29, 2000

Published: June 2000

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Abstract

Consider the Cauchy problem for a hyperbolic $n\times n$ system of conservation laws in one space dimension:

$u_t + f(u)_x = 0$, $u(0,x)=\bar u (x).$ $(CP)$

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 $u=u(t,x)$ which have bounded variation along a suitable family of space-like curves.

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Mathematics Subject Classification: 35L65, 35L45.

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