The Cahn-Hilliard equation, which is important in the context of firstorder phase transition, has frequently been studied in its simplified form, where c{x,t) is a concentration, h(c) is a nonmonotone chemical potential, and K, the coefficient of gradient energy, is a positive constant. In this paper we consider the Cahn-Hilliard equation with nonconstant mobility and gradient energy coefficients, where M(c) and K(c) are assumed to be positive. When K is constant, the free energy functional r rc-co rc E(t) = / / / M~l(c + c0) dc dc dx.