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Information × Registration Number 0222U003684, 0119U100421 , R & D reports Title Singular solutions of mathematical physics equations in anisotropic and heterogeneous media, modeling of diffusion and absorption processes popup.stage_title Head Pasichnyy Mykola O, Кандидат фізико-математичних наук Registration Date 23-05-2022 Organization Bohdan Khmelnytsky National University of Cherkasy popup.description2 Research object – anisotropic elliptical and parabolic equations of diffusion-absorption structure and boundary value problems for them, multi-agent systems, mathematical models of kinetics of diffusion process based on stochastic kinetic mean field method, reaction and interdiffusion processes in binary systems. Purpose of work: to develop new methods of investigation of qualitative properties (in particular, problems of regularity and elimination of singularities) of solutions of anisotropic elliptical and parabolic equations of diffusion-absorption structure and boundary value problems for them with further application, methods of consensus described by dynamic equations on an arbitrary time scale, the development of mathematical and computer models in the evolution of the SKMF method to describe the kinetics of diffusion processes in nanoscale systems, and the development of new models of reaction diffusion for binary systems that take into account nonequilibrium vacancy distribution. in different areas of the diffusion zone. Results and novelty. The problems of existence, representation and regularity of solutions of known boundary value problems of Hilbert, Dirichlet, Neumann, Poincare and Riemann with both continuous and arbitrary measurable boundary data in areas with complex boundary structure for semilinear elliptic equations of potential theory describing processes of diffusion with various chemical and physical absorption both in isotropic and homogeneous, and in anisotropic and inhomogeneous environments are solved. New mathematical and computer models have been developed to describe the kinetics of phase transformations at the atomic level based on the SKMF method. Criteria for selection of phase growth regimes during reaction diffusion taking into account void formation, vacancy sources and sinks are obtained. Product Description popup.authors Babenko Serhii V. Buryachenko Kateryna O. Gusak Andriy M. Kornienko Semen V. Pasichnyy Mykola O. Ryazanov Volodymyr I. popup.nrat_date 2022-05-23 Close