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March  2010, 5(1): 163-188. doi: 10.3934/nhm.2010.5.163

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, Montenegro

Received  July 2009 Revised  December 2009 Published  February 2010

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: 35L6.
Citation: Darko Mitrovic. Existence and stability of a multidimensional scalar conservation law with discontinuous flux. Networks & Heterogeneous Media, 2010, 5 (1) : 163-188. doi: 10.3934/nhm.2010.5.163
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