The Cahn-Hilliard equation is a fourth-order nonlinear stiff partial differential equation describing the phase separation process by which the two components of a binary fluid spontaneously separate and form a domain pure in each component. The mathematical form is given in the picture in which M is the mobility, epsilon is the thickness of the interface and grad^2 is the Laplacian. Furthermore, this equation satisfies the mass conservation property, and the equilibrium solution of this equation is given by phi(x)=tanh(x/sqrt(2*epsilon)). I have found two kinds of papers in which some are claiming that it satisfies the maximum principle (https://arxiv.org/pdf/2111.07313.pdf, https://www.researchgate.net/publication/348746677_Maximum_principle_of_optimal_control_of_a_Cahn-Hilliard-Navier-Stokes_model_with_state_constraints) while other are saying that it does not meet this principle (https://www.mdpi.com/2227-7390/8/8/1224). Expert opinions from senior researchers and professors will be highly appreciated.