Bressan, Alberto; Lewicka, Marta A uniqueness condition for hyperbolic systems of conservation laws. (English) Zbl 1157.35421 Discrete Contin. Dyn. Syst. 6, No. 3, 673-682 (2000). Summary: Consider the Cauchy problem for a hyperbolic \(n\times n\) system of conservation laws in one space dimension: \(u_t+ f(u)_x= 0\), \(u(0,x) = \overline{u}(x).\) (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. Cited in 8 Documents MSC: 35L65 Hyperbolic conservation laws 35L45 Initial value problems for first-order hyperbolic systems PDF BibTeX XML Cite \textit{A. Bressan} and \textit{M. Lewicka}, Discrete Contin. Dyn. Syst. 6, No. 3, 673--682 (2000; Zbl 1157.35421) Full Text: DOI OpenURL