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Information × Registration Number 0122U002463, ( 0223U000224  0223U005771  ) R & D request Title Boundary-Value Problems and Impulse Perturbations of Nonlinear Evolution Equations in Infinite-Dimensional Spaces Head Boichuk Oleksandr А., Доктор фізико-математичних наук Registration Date 09-05-2022 Organization Department for special training National academy of science of Ukraine at Kiev University popup.description1 Analysis of the qualitative behavior of solutions of impulse and stochastically perturbed infinite-dimensional systems. The main attention will be paid to classes of evolution equations without the uniqueness of the solution of the initial problem, such as systems of reaction-diffusion and equations of thin lamina. The conditions of global solvability, the asymptotic behavior of solutions in terms of the existence of invariant measures and the stability of boundary regimes and attractors will be obtained. In particular, for a impulse dynamical system generated by a nonlinear reaction-diffusion system whose trajectories receives impulse perturbation when the energy functional reaches a fixed threshold value, global solvability conditions, existence of a uniform attractor and its propserties will be investigated. For a random dynamical system generated by a stochastically perturbed equation of the thin lamina type, the conditions of global solvability, existence and properties of an invariant measure and a random attractor will be investigated. The asymptotic behavior of stochastic evolutionary functional-differential equations will be studied. In the project, boundary value problems for linear and nonlinear evolution equations in infinite-dimensional spaces of Banach and Hilbert will be considered. Necessary and sufficient solvability conditions of the corresponding boundary-value problem will be obtained. The obtained results will be applied to the study of boundary-value problems for countable systems of ordinary differential equations with periodic and more general boundary conditions. In particular, the evolution equation, which is a generalization of Van der Paul's equation in the case of the Banach and Hilbert spaces, will be investigated. Resonant (irregular) boundary-value problems will be studied. popup.nrat_date 2024-12-09 Close