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 → + ∞.
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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. 191–210DOI 10.4171/PM/1840