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Acta Applicandae Mathematicae

, Volume 113, Issue 1, pp 75–100 | Cite as

Analyticity and Smoothing Effect for the Coupled System of Equations of Korteweg-de Vries Type with a Single Point Singularity

  • Margareth S. Alves
  • Bianca M. R. Calsavara
  • Jaime E. Muñoz Rivera
  • Mauricio SepúlvedaEmail author
  • Octavio Vera Villagrán
Article

Abstract

Using Bourgain spaces and the generator of dilation P=3t t +x x , which almost commutes with the linear Korteweg-de Vries operator, we show that a solution of the initial value problem associated for the coupled system of equations of Korteweg-de Vries type which appears as a model to describe the strong interaction of weakly nonlinear long waves, has an analyticity in time and a smoothing effect up to real analyticity if the initial data only have a single point singularity at x=0.

Keywords

Evolution equations Bourgain space Smoothing effect 

Mathematics Subject Classification (2000)

35Q53 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Margareth S. Alves
    • 1
  • Bianca M. R. Calsavara
    • 2
  • Jaime E. Muñoz Rivera
    • 3
  • Mauricio Sepúlveda
    • 4
    Email author
  • Octavio Vera Villagrán
    • 5
  1. 1.Departamento de MatemáticaUniversidade Federal de Viçosa-UFVViçosaBrazil
  2. 2.Universidade Estadual de Campinas-UnicampLimeiraBrazil
  3. 3.National Laboratory for Scientific ComputationRio de JaneiroBrazil
  4. 4.CI²MA and Departamento de Ingeniería MatemáticaUniversidad de ConcepciónConcepciónChile
  5. 5.Departamento de MatemáticaUniversidad del Bío-BíoConcepciónChile

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