Global Attractor for the Generalized Dissipative KDV Equation with Nonlinearity

We discuss global attractor for the generalized dissipative KDV equation with nonlinearity under the initial conditionu(x,0)=u0(x). We prove existence of a global attractor in spaceH2(Ω), by using decomposition method with cut-off function andKuratowskiα-measure in order to overcome the noncompactness of the classical Sobolev embedding.