English

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 RN\mathbb{R}^{N}. 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}
}