Applied Mathematics and Differential Equations

Local and global invariants of dynamic systems, formal normal forms of dynamic systems and formal maps, local classifications of singularities, solvability of differential and functional equations on smooth manifolds, finite dimensional linear analysis, infinite dimensional nonlinear analysis.

Differential Equations, differential-functional and difference equations

Functional analysis: Sobolev spaces, global analysis: analysis on manifolds and L2-cohomology, geometrical theory of functions: quasi-conformal mappings, chemical engineering science.

Partial and ordinary differential Equations, intergral differential equations, stability of oscillatory systems, control systems

Free boundary and variational problems, numerical methods, mathematical modeling, granular mechanics, applied super- conductivity

Partial differential equations, geometric measure theory

Unsteady-state problems of mathematical physics, mathematical modelling of wave and fracture propagation in solids and structures, dynamic strength and stability of composites under impact. Mathematical models of penetration processes and protective structure optimal design.

Theory of nonlinear transport processes in continuous media, specific interests: mass and momentum transfer in electrolyte solutions, synthetic ion-exchange membranes, reaction-diffusion, free boundary problems in heat and mass transfer.

Functional differential equations and their applications in spectral theory of Schroedinger operator, dynamical systems and probability theory.

Differential equations, asymptotic theory of differential operators

Dualitative properties of partial differential equations. mathematical models of water disalination by electro-dialysis

Besov spaces, sobolev spaces.