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# Solutions with large total variation to nonconservative hyperbolic systems

• In this note we prove the existence of solutions for a class of first order non-linear hyperbolic systems. Given a possibly non conservative straight line system, we prove that all hyperbolic systems sufficiently near to the given one also admit global solutions. The total variation of the initial data is not assumed to be small. Stability estimates are also provided.
Mathematics Subject Classification: 35L45, 35L65.

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