Inserted: 13 jun 2017
Last Updated: 7 jan 2020
Journal: Networks and Heterogeneous Media
The topics discussed in this paper are a reworking of those contained in part of my master thesis. Thus, I thank Professor Andrea Braides for his careful help and his ideas that made this work possible.
We modify the De Giorgi's minimizing movements scheme for a functional, by perturbing the dissipation term, and find a condition on the perturbations which ensures the convergence of the scheme to an absolutely continuous perturbed minimizing movement. The perturbations produce a variation of the metric derivative of the minimizing movement. This process is formalized by the introduction of the notion of curve of maximal slope with a given rate. We show that if we relax the condition on the perturbations we may have many different meaningful effects; in particular, some perturbed minimizing movements may explore different potential wells.
Keywords: Gradient flows, minimizing movements, perturbations