MATHEMATICA BOHEMICA, Vol. 139, No. 4, pp. 607-619, 2014

BV solutions of rate independent differential inclusions

Pavel Krejčí, Vincenzo Recupero

Pavel Krejčí, Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic, e-mail:; Vincenzo Recupero, Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 101 29 Torino, Italy, e-mail:

Abstract: We consider a class of evolution differential inclusions defining the so-called stop operator arising in elastoplasticity, ferromagnetism, and phase transitions. These differential inclusions depend on a constraint which is represented by a convex set that is called the characteristic set. For BV (bounded variation) data we compare different notions of BV solutions and study how the continuity properties of the solution operators are related to the characteristic set. In the finite-dimensional case we also give a geometric characterization of the cases when these kinds of solutions coincide for left continuous inputs.

Keywords: differential inclusion; stop operator; rate independence; convex set

Classification (MSC 2010): 34A60, 74C05, 52B99

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