$\rm BV$ solutions of rate independent differential inclusions

Krejčí, Pavel ; Recupero, Vincenzo

Mathematica Bohemica, Tome 139 (2014) no. 4, pp. 607-619

Abstract (VO)

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 $\rm BV$ (bounded variation) data we compare different notions of $\rm BV$ 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.

Détail

DOI : 10.21136/MB.2014.144138

Classification : 34A60, 34G25, 52B99, 74C05
Keywords: differential inclusion; stop operator; rate independence; convex set

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