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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.

##### MSC:
 35L65 Hyperbolic conservation laws 35L45 Initial value problems for first-order hyperbolic systems 35L60 First-order nonlinear hyperbolic equations
##### Keywords:
Riemann problem; BV solutions
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