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September  2008, 7(5): 1077-1090. doi: 10.3934/cpaa.2008.7.1077

Hyperbolic balance laws with a dissipative non local source

Rinaldo M. Colombo 1, and  Graziano Guerra 2,

1. 

Dipartimento di Matematica, Via Branze, 38 – 25123 Brescia, Italy
2. 

Dipartimento di Matematica e Applicazioni, Via Bicocca degli Arcimboldi, 8 – 20126 Milano, Italy

Received  October 2007 Revised  March 2008 Published  June 2008

This paper considers systems of balance law with a dissipative non local source. A global in time well posedness result is obtained. Estimates on the dependence of solutions from the flow and from the source term are also provided. The technique relies on a recent result on quasidifferential equations in metric spaces.
Keywords: Balance Laws, hyperbolic conservation laws..
Mathematics Subject Classification: Primary: 35L6.
Citation: Rinaldo M. Colombo, Graziano Guerra. Hyperbolic balance laws with a dissipative non local source. Communications on Pure and Applied Analysis, 2008, 7 (5) : 1077-1090. doi: 10.3934/cpaa.2008.7.1077
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