# American Institute of Mathematical Sciences

January  2010, 9(1): 47-60. doi: 10.3934/cpaa.2010.9.47

## Solutions with large total variation to nonconservative hyperbolic systems

 1 Dipartimento di Matematica, Via Branze, 38 – 25123 Brescia, Italy 2 Dip. di Matematica e Applicazioni, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italy

Received  December 2008 Revised  May 2009 Published  October 2009

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.
Citation: Rinaldo M. Colombo, Francesca Monti. Solutions with large total variation to nonconservative hyperbolic systems. Communications on Pure & Applied Analysis, 2010, 9 (1) : 47-60. doi: 10.3934/cpaa.2010.9.47
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