10 citations · 10 across the 5 of their papers we have counts for
5 papers
Finite-dimensional reduction of systems of nonlinear diffusion equations
A. V. Romanov
We present a class of one-dimensional systems of nonlinear parabolic equations for which long-time phase dynamics can be described by an ODE with a Lipschitz vector field in R^n. I…
Final Dynamics of Systems of Nonlinear Parabolic Equations on the Circle
A. V. Romanov
We consider the class of dissipative reaction-diffusion-convection systems on the circle and obtain conditions under which the final (at large times) phase dynamics of a system can…
Ergodic Properties of Tame Dynamical Systems
A. V. Romanov
We study the problem on the weak-star decomposability of a topological -dynamical system , where is an endomorphism of a metric compact set , into erg…
On the Hyperbolicity Properties of Inertial Manifolds of Reaction--Diffusion Equations
A. V. Romanov
For 3D reaction--diffusion equations, we study the problem of existence or nonexistence of an inertial manifold that is normally hyperbolic or absolutely normally hyperbolic. We pr…
Ergodic Properties of Discrete Dynamical Systems and Enveloping Semigroups
A. V. Romanov
For a continuous semicascade on a metrizable compact set , we consider the weak convergence of generalized operator ergodic means in . We discuss…