4 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…