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Information × Registration Number 0223U002213, 0121U109988 , R & D reports Title Qualitative analysis, control and approximation methods in incorrect and nonlocal deterministic and stochastic evolution problems popup.stage_title Head Stanzhytskyi Oleksandr M., Доктор фізико-математичних наук Registration Date 13-02-2023 Organization Taras Shevchenko National University of Kyiv popup.description2 Research object: parabolic equations with nonlocal degenerate diffusion, stochastic systems with nonlocal two-domain operators and delay, evolution equations and inclusions, dissipative reaction-diffusion systems, and nonlinear wave equations with nonsmooth interaction functions. The purpose of the work: parabolic equations with non-local degenerate diffusion, stochastic systems with non-local two-domain operators and delay, evolutionary equations and inclusions, dissipative reaction-diffusion systems and nonlinear wave equations with non-smooth interaction functions. Research methods: methods of infinite dimensional nonlinear and multivalued analysis, methods of normal forms, integral manifolds, global attractors. Theorems on the existence of strong local and global solutions of stochastic equations with a two-domain operator are proved. The carrier of an invariant measure in the corresponding Sobolev spaces was investigated, and the behavior of such measures under random disturbances The principle of large deviations was obtained. Theorems for the existence of solutions and invariant measures for infinite-dimensional stochastic functional-differential equations of the neutral type have been obtained. The existence conditions for the stochastic equations of diffusion aggregation of soft and weak global solutions have been obtained. Conditions for the existence of global attractors have been obtained for a wide class of dissipative systems. Theorems about their stability in relation to external disturbances have been proved, and corresponding estimates of robustness have been obtained.  Product Description popup.authors Hritsenko Nataliya V. Kapustyan Oleksiy V. Kasimova Nina V. Pankov Andrii V. Perestyuk Yuri М. Ryzhov Anton Yu. popup.nrat_date 2023-02-13 Close