Hyperbolic balance laws with a dissipative non local source

Rinaldo M. Colombo; Graziano Guerra

doi:10.3934/cpaa.2008.7.1077

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2008, Volume 7, Issue 5: 1077-1090. Doi: 10.3934/cpaa.2008.7.1077

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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
2.
Dipartimento di Matematica e Applicazioni, Via Bicocca degli Arcimboldi, 8 – 20126 Milano

Received: October 2007

Revised: March 2008

Published: September 2008

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Abstract

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: 35L65.

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