Truncated nonconvex state-dependent sweeping process: implicit and semi-implicit adapted Moreau's catching-up algorithms (Q1615324)

The author studies a nonconvex state-dependent sweeping process in the general Hilbert space, which is the generalization of the classical sweeping process introduced by \textit{J. J. Moreau} [in: Trav. Semin. d'Anal. convexe, Montpellier, Vol. 1, Expose No. 15, 43 p. (1971; Zbl 0343.49019)]. Under some conditions on the perturbation, existence results for the corresponding differential inclusion are developed by adapting Moreau's catching-up algorithms for two schemes, the measure of noncompactness and fixed point theorem for condensing mapping.