Abstract
The following problem arises from the theory of elastoplastic mechanical systems. Let $H$ be a real Hilbert space. Let $I$ be an interval of $\mathbb{R}$ containing its origin $t_ 0$ but not necessarily bounded nor closed on the right. One gives a multifunction (i.e., a set-valued mapping) $t\to C(t)$ from $I$ into $H$, such that the sets $C(t)$ are nonempty closed and convex. When the language of kinematics is used, $t$ is interpreted as the time and $C$ is called a moving set.