On a nonlocal viscous phase separation model
Mohammad Hassan Farshbaf Shaker · 2007
A nonlocal viscous model of phase separation is presented. It is derived from a minimization of free energy containing a nonlocal part due to particle interaction. In contrast to the classical Cahn-Hilliard theory with higher order terms this leads to an evolution system of second order parabolic equations for the particle densities, coupled by nonlocal drift and viscosity terms, which allow reasonable bounds for the concentrations. Applying fixed-point arguments and compactness results we prove the existence of variational solutions in standard Hilbert spaces for evolution systems. Using the free energy as Lyapunov functional the asymptotic state of the system is investigated and characterized by a variational principle.