New entropy conditions for scalar conservation laws with discontinuous flux

Darko Mitrovic

doi:10.3934/dcds.2011.30.1191

Article Contents

2011, Volume 30, Issue 4: 1191-1210. Doi: 10.3934/dcds.2011.30.1191

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New entropy conditions for scalar conservation laws with discontinuous flux

Darko Mitrovic^1,

1.
Faculty of Mathematics, University of Montenegro, Cetinjski put bb, 81000 Podgorica

Received: April 2010

Revised: July 2010

Published: October 2011

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Abstract

We propose new Kruzhkov type entropy conditions for one dimensional scalar conservation law with a discontinuous flux. We prove existence and uniqueness of the entropy admissible weak solution to the corresponding Cauchy problem merely under assumptions on the flux which provide the maximum principle. In particular, we allow multiple flux crossings and we do not need any kind of genuine nonlinearity conditions.

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Mathematics Subject Classification: Primary: 35L65.

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