
Journal of Convex Analysis 27 (2020), No. 3, 10151032 Copyright Heldermann Verlag 2020 What is the Best Viscous Approximation to a RateIndependent Process? Pavel Krejcí Faculty of Civil Engineering, Czech Technical University, 16629 Praha 6, Czech Republic and: Institute of Mathematics, Czech Academy of Sciences, 11567 Praha 1, Czech Republic pavel.krejci@cvut.cz Giselle A. Monteiro Institute of Mathematics, Czech Academy of Sciences, 11567 Praha 1, Czech Republic gam@math.cas.cz Viscous approximations of a rateindependent process with regulated inputs are considered with a general viscosity operator. It is shown that the limit as the viscosity coefficient tends to zero defines a continuous rateindependent inputoutput mapping with respect to the uniform topology in the space of regulated functions, the limits are, however, in general different for different viscosity operators. Examples show that if the viscosity operator is chosen independently of the energy potential, the limit jump trajectories may violate both the normality rule and the maximal dissipation principle. Keywords: Sweeping process, vanishing viscosity. MSC: 49J40, 47J22. [ Fulltextpdf (178 KB)] for subscribers only. 