Research Projects
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Sustainable development means development in which the impact of humanity on the environment does not go beyond the natural possibilities of nature.
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The main idea of the project: research of new classes of differential and functional-differential equations, inequalities and systems and the application of the obtained results to interdisciplinary research in mathematical models of physical and biological processes.
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Many problems that are studied in mathematical analysis can be reformulated in terms of the action of various operators in function spaces.
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Construction of spherically symmetric stationary solutions of the Vlasov-Poisson system of equations describing the stationary distribution of particles in a gravitational field. Obtaining sufficient conditions for confining high-temperature plasma in a “mirror-trap” fusion reactor.
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In the problem of describing the asymptotic properties of generalized solutions of quasilinear parabolic equations in a neighborhood of the time of the singular exacerbation of the boundary regime (i.e. boundary data), at the present time, it were found limiting restrictions on the intensity of the exacerbation leading to solutions with a non zero but finite measure of the blow- up, i.e. the so-called S-modes are described.
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Development and research of blood clotting models and description of thrombin production in normal and pathological (hemophilia) cases; comparison with experimental data.
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The project aims to explore a number of interconnected challenges of modern theory of elliptic operators on manifolds with the actions of groups.
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The project analyzes boundary value problems for elliptic functional-differential equations in bounded domains and half-space, as well as elliptic functional-differential equations in the entire space R^n.
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In order to adequately select drugs and their dosage regimen (improving pharmacotherapy), the diagnostics of the cytochrome Р450 (CYP450) isoenzymes activity is of great importance.