where M η η is the mobility, f is a double-well potential, η η ¯ ¯ is the control on the state variable at the portion of the boundary ∂ ∂ η η Ω Ω , q is the source control at ∂ ∂ q Ω Ω , η η o is the initial condition, and m is the outward normal to ∂ ∂ Ω Ω .