Global stabilization of the generalized Korteweg-de Vries equation

Abstract. This paper is concerned with the internal stabilization of the generalized Korteweg– de Vries equation on a bounded domain. The global well-posedness and the exponential stability are investigated when the exponent in the nonlinear term ranges over the interval [1, 4). The global exponential stability is obtained whatever the location where the damping is active, confirming positively a conjecture of Perla Menzala, Vasconcellos, and Zuazua [Quart. Appl. Math., 60 (2002), pp. 111–129]. Key words. generalized Korteweg–de Vries equation, unique continuation property, smoothing effect, Carleman estimat