JournalspmVol. 66, No. 2pp. 191–210

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

A subscription is required to access this article.

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 → + ∞.

Cite this article

Eleni Bisognin, Vanilde Bisognin, Jardel Morais Pereira, Exponential stabilization of periodic solutions of a system of KdV equations. Port. Math. 66 (2009), no. 2, pp. 191–210

DOI 10.4171/PM/1840