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Unique solutions of \(2\times 2\) conservation laws with large data. (English) Zbl 0852.35092
For a \(2\times 2\) hyperbolic system of conservation laws, a Riemann problem with arbitrarily large data is first considered. A stability assumption is introduced, which yields the existence of a Lipschitz semigroup of solutions, defined on a domain containing all suitably small BV perturbations of the Riemann data. A uniqueness result for large BV solutions is then established. This result is valid within the same class of functions where the existence theorem is proved.

35L65 Hyperbolic conservation laws
35L45 Initial value problems for first-order hyperbolic systems
35L60 First-order nonlinear hyperbolic equations
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