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

Abstract

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