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Networks and Heterogeneous Media

2016, Volume 11, Issue 2: 251-262. doi: 10.3934/nhm.2016.11.251
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Non-critical fractional conservation laws in domains with boundary

  • 1.
    Laboratoire de Mathématiques de Besancon U.F.R. S.T, 16 route de Gray, 25030 BESANCON
  • Received: 01 May 2015 Revised: 01 July 2015

  • 35B30, 35L65, 35L82, 35S10, 35S30.

  • We study bounded solutions for a multidimensional conservation law coupled with a power s∈(0,1) of the Dirichlet laplacian acting in a domain. If s≤1/2 then the study centers on the concept of entropy solutions for which existence and uniqueness are proved to hold. If s>1/2 then the focus is rather on the C∞-regularity of weak solutions. This kind of results is known in RN but perhaps not so much in domains. The extension given here relies on an abstract spectral approach, which would also allow many other types of nonlocal operators.

    Citation: Matthieu Brassart. Non-critical fractional conservation laws in domains with boundary[J]. Networks and Heterogeneous Media, 2016, 11(2): 251-262. doi: 10.3934/nhm.2016.11.251

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  • We study bounded solutions for a multidimensional conservation law coupled with a power s∈(0,1) of the Dirichlet laplacian acting in a domain. If s≤1/2 then the study centers on the concept of entropy solutions for which existence and uniqueness are proved to hold. If s>1/2 then the focus is rather on the C∞-regularity of weak solutions. This kind of results is known in RN but perhaps not so much in domains. The extension given here relies on an abstract spectral approach, which would also allow many other types of nonlocal operators.


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  • This article has been cited by:

    1. Boris Andreianov, Matthieu Brassart, Uniqueness of entropy solutions to fractional conservation laws with “fully infinite” speed of propagation, 2020, 268, 00220396, 3903, 10.1016/j.jde.2019.10.008
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