On the Approximate Controllability for Higher Order Parabolic Nonlinear Equations of Cahn-Hilliard Type

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We prove the approximate controllability property for some higher order parabolic nonlinear equations of Cahn-Hilliard type when the nonlinearity is of sublinear type at infinity. We also give a counterexample showing that this property may fail when the nonlinearity is of superlinear type.