Calculus of Variations and Geometric Measure Theory

G. Scilla - F. Solombrino

A variational approach to the quasistatic limit of viscous dynamic evolutions in finite dimension

created by scilla on 29 May 2018
modified on 21 Nov 2019


Published Paper

Inserted: 29 may 2018
Last Updated: 21 nov 2019

Journal: J. Differential Equations
Volume: 267
Pages: 6216-6264
Year: 2019
Doi: 10.1016/j.jde.2019.06.018

ArXiv: 1805.11389 PDF


In this paper we study the vanishing inertia and viscosity limit of a second order system set in an Euclidean space, driven by a possibly nonconvex time-dependent potential satisfying very general assumptions. By means of a variational approach, we show that the solutions of the singularly perturbed problem converge to a curve of stationary points of the energy and characterize the behavior of the limit evolution at jump times. At those times, the left and right limits of the evolution are connected by a finite number of heteroclinic solutions to the unscaled equation.

Keywords: singular perturbations, Variational methods, Balanced Viscosity solutions, vanishing inertia and viscosity limit, quasistatic limit