Final Dynamics of Systems of Nonlinear Parabolic Equations on the Circle
Analysis of PDEs
2021-04-06 v3 Dynamical Systems
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 . Precisely in this class, the first example of a parabolic problem of mathematical physics without the indicated property was recently constructed.
Keywords
Cite
@article{arxiv.2011.01822,
title = {Final Dynamics of Systems of Nonlinear Parabolic Equations on the Circle},
author = {A. V. Romanov},
journal= {arXiv preprint arXiv:2011.01822},
year = {2021}
}