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Dispersive and diffusive limits for Ostrovsky–Hunter type equations

  • Giuseppe Maria CocliteEmail author
  • Lorenzo di Ruvo
Article

Abstract

We consider the equation
$$\partial _{x}(\partial_{t} u+\partial_{x} f(u)-\beta \partial_{xxx}^{3} u)=\gamma u,$$
that includes the short pulse, the Ostrovsky–Hunter, and the Korteweg–deVries ones. We consider here the asymptotic behavior as \({\gamma\to 0}\) . The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L p setting.

Mathematics Subject Classification

35G25 35L65 35L05 

Keywords

Singular limit Compensated compactness Ostrovsky–Hunter equation Entropy condition 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BariBariItaly

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