Final dynamics of systems of nonlinear parabolic equations on the circle

Abstract

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 be described by an ODE with Lipschitz vector field in RN. Precisely in this class, the first example of a parabolic problem of mathematical physics without the indicated property was recently constructed.

Keywords

• reaction-diffusion-convection equations
• finite-dimensional dynamics on attractor
• inertial manifold