This paper addresses analytical investigations of degenerating PDE systems for phase separation and damage processes considered on nonsmooth time-dependent domains with mixed boundary conditions for the displacement field. The evolution of the system is described by a degenerating Cahn-Hilliard equation for the concentration, a doubly nonlinear differential inclusion for the damage variable and a quasi-static balance equation for the displacement field. The analysis is performed on a time-dependent domain which characterizes the nondegenerated elastic material regions. We choose a notion of weak solutions which consists of weak formulations of the Cahn-Hilliard system and the momentum balance equation, a variational inequality for the damage evolution and an energy inequality. For the introduced degenerating system, we prove global-in-time existence of weak solutions. The main results are sketched from our recent paper [WIAS preprint no. 1759 (2012)].
Self-organization in a polymer system appears when a balance is achieved between long-range repulsive and short-range attractive forces between the chemically different building blocks. Block copolymers forming supramolecular assemblies in aqueous media represent materials which are extremely useful for the construction of drug delivery systems especially for cancer applications. Such formulations suppress unwanted physicochemical properties of the encapsulated drugs, modify biodistribution of the drugs towards targeted delivery into tissue of interest and allow triggered release of the active cargo. In this review, we focus on general principles of polymer selforganization in solution, phase separation in polymer systems (driven by external stimuli, especially by changes in temperature, pH, solvent change and light) and on effects of copolymer architecture on the self-assembly process., M. Hrubý, S. K. Filippov, P. Štěpánek., and Obsahuje bibliografii