Regularization of nonconvex sweeping process in Hilbert space (Q931424)

This paper is concerned with the of solution for the follwing sweeping process \[ u'(t)\in -N_{C(t)}(u(t)), \] \[ u(T_0)=a\in C(T_0), \] where \([T_0,T)\) is an interval of \(\mathbb R,\) \(C(t)\) is a closed subset of a Hilbert space \(H\) for each \(t\in[T_0,T],\) and \(u(T_0)=a\) is the initial condition. Under the Lipschitzian variation of the set-valued mapping \(C(.)\) and under the prox-regularity assumption of \(C(.),\) the author proves the existence and uniqueness of a solution to the problem above.