JournalspmVol. 66 / No. 2DOI 10.4171/pm/1840

Exponential stabilization of periodic solutions of a system of KdV equations

  • Eleni Bisognin

    Centro Universitário Franciscano, Santa Maria, Brazil
  • Vanilde Bisognin

    Centro Universitário Franciscano, Santa Maria, Brazil
  • Jardel Morais Pereira

    Universidade Federal de Santa Catarina, Florianopolis, Brazil
Exponential stabilization of periodic solutions of a system of KdV equations cover

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Abstract

We consider a coupled nonlinear dispersive system of Korteweg–de Vries type in the presence of a dissipative mechanism. First we prove that the Cauchy problem is globally well posed in a suitable periodic Sobolev space and our main result says that the L2 and L∞ norms of the solutions decay exponentially fast as t → + ∞.