Global attractor and stabilization for a coupled PDE-ODE system
Analysis of PDEs
2011-10-11 v1 Dynamical Systems
Abstract
We study the asymptotic behavior of solutions of one coupled PDE-ODE system arising in mathematical biology as a model for the development of a forest ecosystem. In the case where the ODE-component of the system is monotone, we establish the existence of a smooth global attractor of finite Hausdorff and fractal dimension. The case of the non-monotone ODE-component is much more complicated. In particular, the set of equilibria becomes non-compact here and contains a huge number of essentially discontinuous solutions. Nevertheless, we prove the stabilization of any trajectory to a single equilibrium if the coupling constant is small enough.
Cite
@article{arxiv.1110.1837,
title = {Global attractor and stabilization for a coupled PDE-ODE system},
author = {Messoud Efendiev and Sergey Zelik},
journal= {arXiv preprint arXiv:1110.1837},
year = {2011}
}