# Singular perturbations of finite dimensional gradient flows

created by zanini on 19 Jul 2006
modified on 02 Jun 2007

[BibTeX]

Published Paper

Inserted: 19 jul 2006
Last Updated: 2 jun 2007

Journal: Discrete Contin. Dyn. Syst. Ser. A
Volume: 18
Pages: 657-675
Year: 2007

Abstract:

In this paper we give a description of the asymptotic behavior, as $\epsilon\to 0$, of the $\epsilon$-gradient flow in the finite dimensional case.

Under very general assumptions we prove that it converges to an evolution obtained by connecting some smooth branches of solutions to the equilibrium equation (slow dynamics) through some heteroclinic solutions of the gradient flow (fast dynamics).