Global stabilization of a coupled system of two generalized korteweg-de vries type equations posed on a finite domain

The purpose of this work is to study the internal stabilization of a coupled system of two generalized Korteweg-de Vries equations under the effect of a localized damping term. The exponential stability, as well as, the global existence of weak solutions are investigated when the exponent in the nonlinear term ranges over the interval [1, 4). To obtain the decay we use multiplier techniques combined with compactness arguments and reduce the problem to prove a unique continuation property for weak solutions. Here, the unique continuation is obtained via the usual Carleman estimate.