On Global Attractors of Multivalued Semiprocesses and Nonautonomous Evolution Inclusions

In this paper we define multivalued semiprocesses and give theorems providing the existence of global attractors for such systems. This theory generalizes the construction of nonautonomous dynamical systems given by V. V. Chepyzhov and M. I. Vishik to the case where the system is not supposed to have a unique solution for each initial state. Further, we apply these theorems to nonautonomous differential inclusions of reaction–diffusion type.