On a class of sixth order viscous Cahn-Hilliard type equations (Q1942783)

An initial boundary value problem for a class of sixth order viscous Cahn-Hilliard type equations with nonlinear diffusion is considered. Such type problem arises in phase-field modeling of various spatial structures, for example in oil-water-surfactant mixtures and modeling of crystal growth on atomic length, known as phase field cristal model. It is proved existence and uniqueness of a global in time regular solution. By means of the Leray-Schauder fixed point theorem the finite time existence is proved. Based on suitable estimates of solutions, the finite time solution is extended step by step on the infinite time interval.