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Well-posedness and Dispersive/Diffusive Limit of a Generalized Ostrovsky–Hunter Equation

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Abstract

We consider a generalized Ostrovsky–Hunter equation and the corresponding generalized Ostrovsky one with nonlinear dispersive effects. For the first equation, we study the well-posedness of entropy solutions for the Cauchy problem. For the second equation, we prove that as the dispersion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the first one. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method.

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Authors and Affiliations

  1. Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, via E. Orabona 4, 70125, Bari, Italy

    Giuseppe Maria Coclite

  2. Dipartimento di Matematica, Università di Bari, via E. Orabona 4, 70125, Bari, Italy

    Lorenzo di Ruvo

Authors
  1. Giuseppe Maria Coclite
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  2. Lorenzo di Ruvo
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Correspondence to Giuseppe Maria Coclite.

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The authors are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

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Coclite, G.M., di Ruvo, L. Well-posedness and Dispersive/Diffusive Limit of a Generalized Ostrovsky–Hunter Equation. Milan J. Math. 86, 31–51 (2018). https://doi.org/10.1007/s00032-018-0278-0

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  • DOI: https://doi.org/10.1007/s00032-018-0278-0

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