Existence and stability of a multidimensional scalar conservation law with discontinuous flux

Darko Mitrovic

doi:10.3934/nhm.2010.5.163

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2010, Volume 5, Issue 1: 163-188. Doi: 10.3934/nhm.2010.5.163

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Existence and stability of a multidimensional scalar conservation law with discontinuous flux

Darko Mitrovic^1,

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

Received: July 2009

Revised: December 2009

Published: March 2010

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Abstract

We prove the existence and stability of an entropy solution to a multidimensional scalar conservation law with discontinuous flux with no genuine nonlinearity assumptions. The proof is based on the corresponding kinetic formulation of the equation under consideration and a "smart" change of an unknown function.

Keywords:

multidimensional scalar conservation law; discontinuous flux; existence and uniqueness; kinetic formulation.

Mathematics Subject Classification: Primary: 35L65.

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