In 55 years, RUDN University has given the world many famous names and important scientific discoveries. For over 15 years, the University has been in the top 10 best universities in Russia for research and innovation.

RUDN University is a recognized large scientific center, a generator of new ideas and developments.

In 2016 the University held a competition of projects with significant achievements in the priority research areas. Each winning project received funding amounting to 10 million rubles for the implementation of its development.

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.

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.

Development and research of blood clotting models and description of thrombin production in normal and pathological (hemophilia) cases; comparison with experimental data.

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.

To study linear elliptic differential-difference equations, symmetrized matrices corresponding to difference operators are used, while the skew-symmetric component does not violate the strong ellipticity of the linear operator and the smoothness properties of generalized solutions. Previously, the solvability criteria for nonlinear elliptic differential-difference equations were proposed, in which the difference operators are described by symmetric matrices. It was shown that, unlike the linear case for nonlinear problems, the skew-symmetric part affects ellipticity. In this project, we propose to use previously developed methods to study nonlinear elliptic problems with difference operators, which correspond to triangular matrices.

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.

Metabolomic research (studying body responses to pathophysiological effects by assessing the levels of low molecular weight metabolites in biofluids and tissues and their dynamics) forms the basis of the project.

Development of new methods for synthesis of natural compounds and its analogues on a basis of domino-reactions and highly selective reagents to search for new biologically active substances