Fields of interest
Homogenization of partial differential equations.
Homogenization on the Riemannian manifolds
Homogenized models of complex non-newtonian fluids.
Homogenization problems in porous media.
Studying of nonlinear completely integrable evolutional equations:
-- Riemann-Hilbert problem method;
- analysis of initial-boundary value problems;
- long time asymptotics
Vortex motion in superfluids and Bose-Einstein condensates. Variational problems for Ginzburg-Landau functional.
Modeling of the biological systems and their investigation in frame of the determined chaos theory.