A new rapidly developing direction in qualitative theory and the theory of asymptotic
methods for nonlinear partial differential equations, in particular for the viscous
liquid hydrodynamics equations, was originated, i.e. non-local stability theory and
attractor theory for autonomous evolutional problems of dissipative type, as well as
the theory of compact and asymptotically compact semigroups of nonlinear operators
acting in a locally noncompact metric phase space.
A stationary problem with free boundaries for the Navier--Stokes equations and a
problem of evolution of an isolated finite volume of viscous noncontractive liquid
were solved.

The limiting smoothness of generalized solutions of quasilinear parabolic equations
admitting double degeneration was proved.

A theory of solvability of initial-boundary value problems for equations of motion of
linear viscous-elastic liquid was developed.

Binomial asymptotic formulae for the distribution function of eigenvalues and the spectral
function of elliptic selfadjoint differential operator with regular elliptic boundary
conditions on a smooth compact manifold with edge were obtained.