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

  • Received: 01 July 2009 Revised: 01 December 2009
  • Primary: 35L65.

  • 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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  • 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.


  • This article has been cited by:

    1. MIROSLAV BULÍČEK, PIOTR GWIAZDA, AGNIESZKA ŚWIERCZEWSKA-GWIAZDA, MULTI-DIMENSIONAL SCALAR CONSERVATION LAWS WITH FLUXES DISCONTINUOUS IN THE UNKNOWN AND THE SPATIAL VARIABLE, 2013, 23, 0218-2025, 407, 10.1142/S0218202512500510
    2. S. Mishra, 2017, 18, 9780444639103, 479, 10.1016/bs.hna.2016.11.002
    3. Darko Mitrovic, New entropy conditions for scalar conservation laws with discontinuous flux, 2011, 30, 1553-5231, 1191, 10.3934/dcds.2011.30.1191
    4. Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda, Petra Wittbold, Aleksandra Zimmermann, Multi-dimensional scalar balance laws with discontinuous flux, 2014, 267, 00221236, 2846, 10.1016/j.jfa.2014.07.009
    5. Boris Andreianov, Kenneth Hvistendahl Karlsen, Nils Henrik Risebro, A Theory of L 1-Dissipative Solvers for Scalar Conservation Laws with Discontinuous Flux, 2011, 201, 0003-9527, 27, 10.1007/s00205-010-0389-4
    6. Graziano Crasta, Virginia De Cicco, Guido De Philippis, Kinetic Formulation and Uniqueness for Scalar Conservation Laws with Discontinuous Flux, 2015, 40, 0360-5302, 694, 10.1080/03605302.2014.979998
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