Speciality:
01.01.02 (Differential equations, dynamical systems, and optimal control)
E-mail: Keywords: symmetries,
Lie algebras,
integrability,
parabolic equation,
the Navier–Stokes equations,
stabilization of solutions.
Subject:
The criterion of uniform stabilization of solutions to the first mixed problem for a parabolic equation in unbounded domain was established. The decay rate of solutions to the Navier–Stokes equations in unbounded three dimensional domain was established. Jointly with A. A. Bormisov and E. S. Gudkova it was shown that for every hiperbolic system of Riccati type is corresponded by natural way a $Z$-graded Lie algebra. This result permited (jointly with A. A. Bormisov) to describe the symmetries of hiperbolic system of Riccati type corresponded to the affine Kac-Moody algebras.
