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.
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.