Attractors For A Class Of Semi-Linear Degenerate Parabolic Equations With Critical Exponents

We consider degenerate parabolic equation of the form(?)tu(t)= ??u(t)+ f(u)U|(?)n = 0,u|t = 0=u0 in a bounded domain ?(?)RN C RN,and u0 ?W?1,2(?),where the nonlinearity satisfies the critical growth condition and?? is a subelliptic operator of the typeFirst of all,we will obtain the global existence and uniqueness of the solution by Galerkin method;second,split the nonlinearity f into two parts,and verify the properties we need of solutions for corresponding equations.Therefore,we have the global existence of attractor for the equation.