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.
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.
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.
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.