Global Attractor of Nonautonomous Evolution Inclusion of Reaction-Diffusion Type


The present paper considers the nonautonomous evolution inclusion of reaction-diffucion type, whose right part is majorized by continuous functions of step growth, for which additional conditions of translation compactness are imposed. We prove the existence and study the properties of the global attractor of the family of multivalued processes generated by solutions of the inclusion. Relying on the solutions of nonautonomous inclusion with the right part of power growth, we construct the family of multivalued processes. In addition, we prove the existence of the invariant stable connected global attractor for this family in the phase space. It comprises bounded completed trajectories. This proof method can be applied to other classes of problems: evolutional inclusions of the second order and systems of phase–field equations with the multivalued function of interaction.

Publication year: 
С. 98–104., укр., Бібліогр.: 9 назв.

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