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A note on front tracking for the Keyfitz-Kranzer system. (English) Zbl 1316.35192
The authors develop a front tracking method for the \(n\times n\) Keyfitz-Kranzer system \(u_t+(u\phi(|u|))_x=0\) with initial data \(u(0,x)=u_0(x)\in L^\infty(\mathbb{R},\mathbb{R}^n)\) such that \(|u_0(x)|\) is a function of bounded variation. They prove convergence of the approximations to the strong generalized entropy solution of the original problem in the sense of E. Yu. Panov [Sb. Math. 191, No. 1, 121–150 (2000); translation from Mat. Sb. 191, No. 1, 127–157 (2000; Zbl 0954.35107)]. The authors also present numerical examples, which allow to compare the front tracking approximation with approximations computed by some finite difference schemes.

MSC:
35L65 Hyperbolic conservation laws
35L45 Initial value problems for first-order hyperbolic systems
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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