Abstract: By using  a priori estimates of the solution and the asymptotic compactness of the operator semigroup, we considered the global dynamic behavior  of a fourth-order nonlinear evolution equation describing the dynamic controll of crystal growth process, and  proved the existence of global attractor of the equation in H⁴(0,1) space when  the initial value of the equation  belonged to H¹(0,1).

Key words: global attractor, nonlinear evolution equation, global weak solution