Finite-dimensional reduction of systems of nonlinear diffusion equations
Analysis of PDEs
2022-10-04 v1
Abstract
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. In the considered case of the Dirichlet boundary value problem sufficient conditions for a finite-dimensional reduction turn out to be much wider than the known conditions of this kind for a periodic situation.
Cite
@article{arxiv.2210.00499,
title = {Finite-dimensional reduction of systems of nonlinear diffusion equations},
author = {A. V. Romanov},
journal= {arXiv preprint arXiv:2210.00499},
year = {2022}
}