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Global solutions of systems of conservation laws by wave-front tracking. (English) Zbl 0779.35067
The author considers the Cauchy problem for a nonlinear strictly hyperbolic \(n\times n\) system of conservation laws in one space variable \(u_ t+ F(u)x=0\), \(x\in\mathbb{R}\), \(t\geq 0\); \(u(0,x)=v(x)\) with sufficiently small total variation of \(v\) and proves existence of weak global solutions satisfying entropy admissible conditions. Approximate solutions are constructed based on wave-front tracking – the approximate solutions are piecewise constant functions generated by solutions of Riemann problems, starting from piecewise constant approximation of \(v\). It is proved, that total variation remains small and that the number of lines of discontinuities remains finite. Consequently a subsequence converges to a desired solution.
Reviewer: A.Doktor (Praha)

MSC:
35L65 Hyperbolic conservation laws
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35A35 Theoretical approximation in context of PDEs
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