A uniqueness condition for hyperbolic systems of conservation laws. (English) Zbl 1157.35421

Bressan, Alberto; Lewicka, Marta

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.

MSC:

35L65	Hyperbolic conservation laws
35L45	Initial value problems for first-order hyperbolic systems