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Networks and Heterogeneous Media

2016, Volume 11, Issue 2: 281-300. doi: 10.3934/nhm.2016.11.281
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A singular limit problem for conservation laws related to the Kawahara-Korteweg-de Vries equation

  • 1.
    Department of Mathematics, University of Bari, Via E. Orabona 4, I--70125 Bari
  • 2.
    Department of Science and Methods for Engineering, University of Modena and Reggio Emilia, via G. Amendola 2, 42122 Reggio Emilia
  • Received: 01 April 2015 Revised: 01 October 2015

  • Primary: 35G25, 35L65; Secondary: 35L05.

  • We consider the Kawahara-Korteweg-de Vries equation, which contains nonlinear dispersive effects. We prove that as the dispersion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the Burgers equation. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the Lp setting.

    Citation: Giuseppe Maria Coclite, Lorenzo di Ruvo. A singular limit problem for conservation laws related to the Kawahara-Korteweg-de Vries equation[J]. Networks and Heterogeneous Media, 2016, 11(2): 281-300. doi: 10.3934/nhm.2016.11.281

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  • We consider the Kawahara-Korteweg-de Vries equation, which contains nonlinear dispersive effects. We prove that as the dispersion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the Burgers equation. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the Lp setting.


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  • © 2016 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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