This issuePrevious ArticleWeak geodesic flow and global solutions of the Hunter-Saxton equationNext ArticleAction functionals that attain regular minima in presence of energy gaps
Singular perturbations of finite dimensional gradient flows
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).