2018/05/29 by Giovanni Scilla, Scilla, Giovanni, Francesco Solombrino +1
Mathematics · #34K26 #49Q20 #74H10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1805.11389
openalex publication_date 2018/05/29 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
In this paper we study the vanishing inertia and viscosity limit of a second\norder system set in an Euclidean space, driven by a possibly nonconvex\ntime-dependent potential satisfying very general assumptions. By means of a\nvariational approach, we show that the solutions of the singularly perturbed\nproblem converge to a curve of stationary points of the energy and characterize\nthe behavior of the limit evolution at jump times. At those times, the left and\nright limits of the evolution are connected by a finite number of heteroclinic\nsolutions to the unscaled equation.\n