Long-term forecasts for state functions of autonomous inclusions of reaction-diffusion type in Rn
Abstract
The reaction-diffusion equation with multivalued interaction function in an unbounded domain is considered. Conditions on the parameters of the problem do not guarantee the uniqueness of solution for the corresponding Cauchy problem. The problem of the long-term forecasting for the state functions of the investigated problem in sense of the theory of global and trajectory attractors for multivalued semiflows is studied. The problems of existence and properties of weak solutions of autonomous reaction-diffusion inclusion in an unbounded domain are studied. The conditions of existence of global and trajectory attractors in the phase and, therefore, the extended phase space are found, their regularity is set. The obtained results are applied to specific problems that modeling the real processes of different nature. In particular, the models of combustion in a porous medium, model of conduction of electrical impulses in the nerves, climatological models are considered.References
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