Solutions with large total variation to nonconservative hyperbolic systems

Pages: 47 - 60, Volume 9, Issue 1, January 2010

doi:10.3934/cpaa.2010.9.47       Abstract        Full Text (223.7K)       Related Articles

Rinaldo M. Colombo - Dipartimento di Matematica, Via Branze, 38 – 25123 Brescia, Italy (email)
Francesca Monti - Dip. di Matematica e Applicazioni, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italy (email)

Abstract: 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.

Keywords:  First order hyperbolic equations, non-conservative systems, conservation laws.
Mathematics Subject Classification:  35L45, 35L65.

Received: December 2008;      Revised: May 2009;      Published: October 2009.