2016/11/24 by Virginia Agostiniani, Agostiniani, Virginia, Riccarda Rossi +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #34K26 #49Q20 #74H10 #Analysis of PDEs (math.AP) #Caveolin-1 and cellular processes #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1611.08105
openalex publication_date 2016/11/24 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28
In this note we study the singular vanishing-viscosity limit of a gradient\nflow set in a finite-dimensional Hilbert space and driven by a smooth, but\npossibly non convex, time-dependent energy functional. We resort to ideas and\ntechniques from the variational approach to gradient flows and rate-independent\nevolution to show that, under suitable assumptions, the solutions to the\nsingularly perturbed problem converge to a curve of stationary points of the\nenergy, whose behavior at jump points is characterized in terms of the notion\nof Dissipative Viscosity solution. We also provide sufficient conditions under\nwhich Dissipative Viscosity solutions enjoy better properties, which turn them\ninto Balanced Viscosity solutions. Finally, we discuss the generic character of\nour assumptions.\n