Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Weak differentiability of scalar hysteresis operators

Pages: 2405 - 2421, Volume 35, Issue 6, June 2015      doi:10.3934/dcds.2015.35.2405

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Martin Brokate - Fakultät für Mathematik, TU München, Boltzmannstr. 3, D 85747 Garching bei München, Germany (email)
Pavel Krejčí - Institute of Mathematics, Czech Academy of Sciences, Žitná 25, CZ-11567 Praha 1, Czech Republic (email)

Abstract: Rate independent evolutions can be formulated as operators, called hysteresis operators, between suitable function spaces. In this paper, we present some results concerning the existence and the form of directional derivatives and of Hadamard derivatives of such operators in the scalar case, that is, when the driving (input) function is a scalar function.

Keywords:  Hysteresis, rate independence, differentiability, play, Preisach, Prandtl-Ishlinskii, evolution variational inequalities, accumulated maximum, gliding maximum.
Mathematics Subject Classification:  Primary: 47J40, 47T20; Secondary: 34C55, 49J52.

Received: January 2014;      Revised: May 2014;      Available Online: December 2014.