Belan E. Method of invariant manifolds in the theory of parabolic and functional differential equations and its application

The dissertation is devoted to qualitative and bifurcation analysis of some classes of parabolic equations, parabolic functional-differential and differential-difference equations. The study is based on the method of invariant manifolds and its extensions. A new method for investigation of dissipative structure dynamics is developed. The buffer phenomenon in the parabolic problems with small diffusion is also considered. New approches are applied to some models in nonlinear optics and spin combustion theory. Some well known results of quasiperiodic solutions of ODE's are extended to functional-differential equations. In particular, Arnold-Samoilenko-Moser results about the reducibility of ODE's on m-dimentional torus to a pure rotation are extended on differential-difference equations.