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Non-convex second-order Moreau’s sweeping processes in Hilbert spaces. (English) Zbl 1386.34033

Summary: In this paper, we study a differential inclusion known as second-order sweeping process for a class of prox-regular non-convex sets. Assuming that such sets depend continuously on time and state, we give a new proof of the existence of solutions via Schauder’s fixed point theorem and the well-posedness for the perturbed first-order sweeping process in Hilbert spaces.

MSC:

34A60 Ordinary differential inclusions
49J52 Nonsmooth analysis
46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
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