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

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

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

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.
- multidimensional scalar conservation law; discontinuous flux; existence and uniqueness; kinetic formulation
Citation: Darko Mitrovic. Existence and stability of a multidimensional scalar conservation law with discontinuous flux[J]. Networks and Heterogeneous Media, 2010, 5(1): 163-188. doi: 10.3934/nhm.2010.5.163

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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.
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