Pawłow, Irena; Zajączkowski, Wojciech M. On a class of sixth order viscous Cahn-Hilliard type equations. (English) Zbl 1276.35100 Discrete Contin. Dyn. Syst., Ser. S 6, No. 2, 517-546 (2013). 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. Reviewer: Mersaid Aripov (Tashkent) Cited in 17 Documents MSC: 35K35 Initial-boundary value problems for higher-order parabolic equations 35K58 Semilinear parabolic equations Keywords:nonlinear diffusion; oil-water-surfactant mixtures; Leray-Schauder fixed point theorem PDFBibTeX XMLCite \textit{I. Pawłow} and \textit{W. M. Zajączkowski}, Discrete Contin. Dyn. Syst., Ser. S 6, No. 2, 517--546 (2013; Zbl 1276.35100) Full Text: DOI