On a class of sixth order viscous Cahn-Hilliard type equations
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.
scientific article; zbMATH DE number 6144730