Final dynamics of systems of nonlinear parabolic equations on the circle

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 R-N. Precisely in this class, the first example of a parabolic problem of mathematical physics without the indicated property was recently constructed.

Automated summary

This study focuses on dissipative reaction-diffusion-convection systems on the circle and identifies conditions under which the final phase dynamics can be described by an ODE with Lipschitz vector field in R-N. A recent construction of a parabolic problem in mathematical physics within this class lacks the indicated property.