Shkliar T. Investigation of qualitative behaviour of solutions of nonautonomous evolution inclusions

The thesis deals with the global attractors of multi-valued processes, which are generated by non-autonomous evolution inclusions of subdifferential and parabolic types with non-Lipschitz multi-value right side. For the inclusion of subdifferential type properties of solutions, existence and properties of global attractors in the case of nonautonomous multi-valued right part that is not lipschitz on a phase variable and is translation-compact on the time variable in the space of upper semicontinuous multi-valued maps, which have no more than linear growth is considered. Also, the existence and qualitative behaviour of nonnegative solutions were investigated with additional conditions on the multi-valued perturbation. Evolution inclusion of parabolic type with the time dependent main part and multi-valued perturbation of more than linear growth was considered. The multi-valued nonautonomous dynamical system was built on the integral solutions, for which the existence of global attractors in the phase space was proved and its properties were investigated. Evolution inclusions of reaction-diffusion type was considered, where multi-valued right side can has a power-law growth. On the condition of translation compacted functions, which are defined the boundaries of multi-valued perturbations, it was proved that all weak solutions are generated the family of multi-valued processes, for which in phase space there exists invariant, connected, stable global attractor, which consists of complete trajectories.