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Information × Registration Number 0224U002641, 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 22-02-2024 Organization Taras Shevchenko National University of Kyiv popup.description2 Study object: parabolic equations with nonlocal degenerate diffusion, stochastic systems with nonlocal two-domain operators and delay, impulse evolutionary systems, dissipative reaction-diffusion systems, nonlinear wave equations with non-smooth interaction functions, controlled systems with singular coefficients. Study goal: obtaining new qualitative and quantitative characteristics of a wide class of mathematical models of real objects, including models of thin films, Burgers model, heart defibrillator model, population models with "memory". Methods: stochastic evolutionary equations, Galerkin approximations, averaging, infinite-dimensional nonlinear and multivalued analysis, integral manifolds, global attractors. For functional differential equations (FDEs) of the Fredholm integral type, the conditions for the existence and unity of the solutions of the boundary value problem are established. Asymptotics have been established, sufficient conditions for controllability at infinite time intervals by systems of impulse equations have been obtained. Theorems on the controllability of evolutionary equations and inclusions with perturbations in the coefficients, the asymptotic behavior of solutions of infinitedimensional stochastic FDEs, and the existence of invariant measures in displacement spaces have been proved. Theorems on the existence of strong local and global solutions of stochastic equations with a two-domain operator are proved. The support of an invariant measure in Sobolev spaces and the behavior of measures under random perturbations are studied. Theorems of existence of solutions and invariant measures for infinitedimensional stochastic FDEs of neutral type, existence conditions for stochastic equations of diffusion aggregation of soft and weak global solutions, conditions of existence of global attractors for a wide class of dissipative systems have been obtained. Product Description popup.authors Oleksii V. Kapustian Kasimova Nina V. Perestiuk Yurii М. Ryzhov Anton Yu. popup.nrat_date 2024-02-22 Close