Attractors for Differential Inclusions and Their Applications for Evolution Algorithms

In this paper we study the issues of global solvability and existence of global attractors for differential inclusion of parabolic type in the phase space of continuous functions with -norm. Assuming an upper semicontinuity of the multi-valued right-hand side and sign condition of dissipativity we prove that all mild-solutions generate a multi-valued semiflow, and establish the existence of global attractor for the semiflow. We present also an evolutional algorithm for finding attractor elements.