On a quasilinear nonlocal Benney system

João Paulo Dias, Filipe Oliveira

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Abstract

We study a quasilinear nonlocal Benney system and establish the existence and uniqueness of strong local in time solutions to the corresponding Cauchy problem. We also show, under certain conditions, the blow-up of such solutions in finite time. Furthermore, we prove the existence of global weak solutions and exhibit bound-state solutions to this system.

Original languageEnglish
Pages (from-to)135-156
Number of pages22
JournalJournal of Hyperbolic Differential Equations
Volume14
Issue number1
DOIs
Publication statusPublished - 1 Mar 2017

Keywords

  • Benney systems
  • Blow-up
  • Bound-state solutions
  • Cauchy problem

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