Journal of Convex Analysis 27 (2020), No. 3, 1015--1032
Copyright Heldermann Verlag 2020
What is the Best Viscous Approximation to a Rate-Independent 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 rate-independent 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 rate-independent input-output 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.
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