Romaniuk I. Attractors of infinite-dimensional impulsive dynamical systems

The thesis is devoted to the generalization of the theory of global attractors of multi-valued infinite-dimensional dynamical systems in case when trajectories of evolution systems have jumps at moments of intersection with certain surfaces of the phase space. The basic principles and results of the theory of global attractors of multi-valued dynamical systems are given and the general scheme of construction of an infinite-dimensional impulsive dynamical system without uniqueness is described. The properties of invariance of the non-impulsive part of the obtained global attractor are also studied in the thesis. The obtained abstract results are used to study the qualitative behavior of solutions of a number of impulsive evolution systems in infinite-dimensional phase spaces. In particular, the theorems on the existence and properties of a global attractor for an impulsive multi-valued dynamical system generated by weakly nonlinear parabolic inclusion, two-dimensional weakly nonlinear parabolic system and wave equation are proved.