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Well-Posedness and Time Regularity for a System of Modified Korteweg-de Vries-Type Equations in Analytic Gevrey Spaces

Author

Listed:
  • Aissa Boukarou

    (Laboratoire de Mathématiques et Sciences Appliquées, Université de Ghardaia, Ghardaia 47000, Algerie)

  • Kaddour Guerbati

    (Laboratoire de Mathématiques et Sciences Appliquées, Université de Ghardaia, Ghardaia 47000, Algerie)

  • Khaled Zennir

    (Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass 51921, Saudi Arabia)

  • Sultan Alodhaibi

    (Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass 51921, Saudi Arabia)

  • Salem Alkhalaf

    (Computer Department, College of Sciences and Arts, Qassim University, Ar-Rass 51921, Saudi Arabia)

Abstract

Studies of modified Korteweg-de Vries-type equations are of considerable mathematical interest due to the importance of their applications in various branches of mechanics and physics. In this article, using trilinear estimate in Bourgain spaces, we show the local well-posedness of the initial value problem associated with a coupled system consisting of modified Korteweg-de Vries equations for given data. Furthermore, we prove that the unique solution belongs to Gevrey space G σ × G σ in x and G 3 σ × G 3 σ in t . This article is a continuation of recent studies reflected.

Suggested Citation

  • Aissa Boukarou & Kaddour Guerbati & Khaled Zennir & Sultan Alodhaibi & Salem Alkhalaf, 2020. "Well-Posedness and Time Regularity for a System of Modified Korteweg-de Vries-Type Equations in Analytic Gevrey Spaces," Mathematics, MDPI, vol. 8(5), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:809-:d:358907
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