Singular perturbations of finite dimensional gradient flows

Details Singular perturbations of finite dimensional gradient flows Singular perturbations of finite dimensional gradient flows

2006-07-19

arxiv.org/abs/math/0607461v1

Mathematics

Functional Analysis

19 pages, 4 figures

Scientific paper

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).

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