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Information × Registration Number 0222U003508, 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 05-04-2022 Organization Taras Shevchenko National University of Kyiv popup.description2 Object of research: parabolic equations with nonlocal degenerate diffusion, stochastic systems with nonlocal bidomain operators and delay, impulse evolutionary systems, dissipative reaction-diffusion systems and nonlinear wave equations with nonsmooth interaction functions, controlled systems with singular coefficients. Objective: to obtain new qualitative and quantitative (including statistical) characteristics for a wide range of mathematical models of real natural objects, including thin film models, Burgers model, cardiac defibrillator model, population models with "memory" and others. Research methods: methods of nonlinear analysis (compactness and monotonicity method), methods of stochastic evolution equations, classical ISS theory for systems of ordinary differential equations, Galerkin approximation method, averaging method. For functional-differential equations of integral type Fredholm established the conditions for the existence and uniqueness of the solutions of the boundary value problem. Sufficient conditions for the existence of optimal controls for systems of differential equations on infinite time scales are obtained. Asymptotics is established and sufficient controllability conditions for systems of impulse equations are obtained at infinite time intervals. The theorems on controllability are proved evolutionary equations and inclusions with perturbations in coefficients. The asymptotic behavior of solutions of infinitely measurable stochastic functional-differential equations has been studied, in particular, the existence of invariant measures in the corresponding shear spaces has been established. Optimal estimates were obtained parameters in the model of dynamic linear regression with delay. Ergotechnical systems in the critical case were studied for the first time by machine learning methods. For impulse systems of parabolic and hyperbolic type with energy jumps, the asymptotic behavior of solutions with respect to the existence of uniform att  Product Description popup.authors Zhuk Tetyana Yu. Kapustyan Oleksiy V. Kasimova Nina V. Klimchuk Taras V. Pereguda Oleg V. Perestyuk Yuri М. Ryzhov Anton Yu. Trotsenko Yaroslav Р. popup.nrat_date 2022-04-05 Close