$\rm BV$ solutions of rate independent differential inclusions
Pavel Krejčı́, Vincenzo Recupero · Mathematica Bohemica · 2014
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.