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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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References:
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