Singular perturbations of finite dimensional gradient flows

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November 2007, 18(4): 657-675. doi: 10.3934/dcds.2007.18.657

Singular perturbations of finite dimensional gradient flows

1.	SISSA, via Beirut 4, 34014 Trieste, Italy

Received September 2006 Revised December 2006 Published May 2007

Abstract
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In this paper we give a description of the asymptotic behavior, as $\varepsilon\to 0$, of the $\varepsilon$-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).

Keywords: gradient flow, heteroclinic solutions., saddle-node bifurcation, singular perturbations.

Mathematics Subject Classification: 34K26, 34K18, 34C3.

Citation: Chiara Zanini. Singular perturbations of finite dimensional gradient flows. Discrete & Continuous Dynamical Systems - A, 2007, 18 (4) : 657-675. doi: 10.3934/dcds.2007.18.657

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