Registration Number
0225U000217,
(0124U003771)
, R & D reports
Title
Infinite-dimensional evolution equations with multivalued and stochastic dynamics
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Параболічні включення, стохастичні рівняння та рівняння тонких плівок: розв'язність та якісна поведінка
Head
Kapustian Oleksii V., Доктор фізико-математичних наук
Registration Date
07-01-2025
Organization
Taras Shevchenko National University of Kyiv
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Study of qualitative behavior, stability of limit regimes and control of solutions of infinite-dimensional equations and inclusions with deterministic and random perturbations. The main attention will be paid to initial-boundary value problems for nonlinear equations and inclusions with stochastic and impulse disturbances, stochastic functional-differential equations, establishment of solvability conditions and regularity of solutions, stability of limit sets, invariant measures, optimal control
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The project is aimed at solving important and topical problems in the qualitative theory of nonlinear partial differential equations, both deterministic and stochastic.
The goal of the project is to study the qualitative behavior, stability of boundary conditions and control of solutions of infinite-dimensional equations and inclusions with deterministic and random disturbances. The main attention is paid to initial-boundary value problems for nonlinear equations and inclusions with stochastic and impulse disturbances, stochastic functional-differential equations, establishing conditions for solvability and regularity of solutions, stability of boundary sets, invariant measures, optimal control.
The objectives of the project are to prove the existence, stability, and robustness of attracting sets for solutions of nonlinear evolutionary equations with multi-valued right-hand sides, to prove the non-emptiness and compactness of attracting sets of multi-valued impulse semi-flows in the case when an infinite number of phase vector coordinates are perturbed, to prove the solvability and justification of the averaging method for optimal control problems of evolutionary equations and inclusions with perturbations in coefficients and stochastic equations in porous media, to study the qualitative behavior of weak solutions of nonlocal equations and thin-film-type systems, to prove the existence and uniqueness of invariant measures for stochastic functional-differential equations of neutral type, to develop new machine learning methods for approximate solution of solutions of quasilinear equations and inclusions with partial derivatives.
Product Description
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Zhuk Tetiana Yu.
Levenchuk Liudmyla B.
Stanzhytskyi Andrii O.
Оleksandr M. Stanzhytskyi
Taranets Roman M.
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2025-01-07
