Existence of solutions to the nonconvex sweeping process
In this paper, the author proves the existence of solutions to the sweeping process problem \[ x'(t)\in-N_{C(t)} \bigl(x(t) \bigr)\text{ a.e. }, x(t)\in C(t),\;x(0)=x_0\in C(0), \] where \(C(\cdot)\) is an arbitrary Hausdorff-Lipschitzian multifunction from \(I=[0,T]\) onto the set of nonempty closed subsets of \(\mathbb{R}^d\). This generalizes a well-known result of \textit{J. J. Moreau} [Rafle par un convexe variable. I. Trav. Sémin. d'Anal. convexe, Montpellier, Vol. 1, Exposé No. 15 (1971; Zbl 0343.49019)].
scientific article; zbMATH DE number 1515444
scientific article