Piotr Kalita: Multivalued dynamical systems and their attractors


For some initial and boundary value problems governed by equations of mathematical physics the solution may be nonunique for a given initial data or the question of the solution uniqueness remains unanswered. Still, it is possible to study such problems from the point of view of the theory of dynamical systems. We present the formalisms which allow to obtain the attractor existence and its properties and we discuss the known results and open problems for autonomous and non-autonomous cases. We illustrate the results by problems from fluid mechanics: Navier-Stokes equations with multivalued boundary conditions and Surface Quasigeostrophic equation.