Some results on classical and quaternionic evolutions problems

Abstract

In this talk I will show some recent results on two evolution problems both connected with the notion of semigroup.
In the first part I will introduce the notion of quaternionic sectorial operator: I will show how this generates an analytic quaternionic semigroup which describes the solutions of first order linear evolution equations in a quaternionic Banach space.
The second part will deal with non-convex Moreau sweeping processes arising in elasto-plasticity and in crowd motion dynamics: they represent a class of nonlinear evolution problems having the semigroup and the rate independence properties. Using both properties I show how to obtain BV solutions by means of a new reparametrization technique for curves with values in the family of closed sets endowed with the Hausdorff distance.