Area of science:
Mathematics, mechanics and informatics.
Mathematics and theoretical physics: modeling of dynamic systems.
The project is devoted to the development of new qualitative and geometric methods for the study of boundary value problems for differential and functional differential equations, their application to the Vlasov equations (kinetics of high-temperature plasma), the Kato problem of the square root of the operator, mathematical biology and mathematical medicine.
- The study of boundary value problems for elliptic functional-differential equations containing in the upper part of compression with incommensurable logarithms.
- To obtain the terms for the unique solvability of the elliptic functional-differential equations with orthotropic contractions in the scale of Kondratiev weight spaces.
- To find classes of elliptic differential-difference equations for which the Dirichlet problem is correct in the half-space, to obtain integral representations and qualitative properties of its solutions.
- The study of Fredholm and index problems of G-operators associated with groups of integral Fourier operators.
- Dynamic properties of spatially discrete and continuous reaction-diffusion systems with hysteresis in the multidimensional case.
- Existence and stability of traveling waves in systems with fast oscillating coefficients.
- The study of the interaction between the nonpotential operators, bivariation and algebraic structures.
- The study of the capability information, calculate the volume of hyperbolic 5-simplex in terms of the lengths of edges by calculating one-dimensional integrals of some elementary functions.
- To find new classes of operators satisfying Kato hypothesis square root from the operator: strongly elliptic functional-differential operators with incommensurable logarithms of argument contractions and elliptic differential-difference equations with degeneration.
- To study stationary solutions of the system of Vlasov-Poisson equations describing the equilibrium state of high-temperature plasma in a thermonuclear reactor, to study the kinetics of high-temperature plasma, as well as the growth of entropy and its consequences in mechanics and kinetics.
- To study the dynamics of distributed systems (in physical space or feature space) describing the interaction of immune cells and pathogens in humans and animals.
- To study of reaction-diffusion waves and pulses to predict thrombosis and spread of infection in tissue.