On Properties of Differential Inclusions with Prox-regular Sets

2016/06/16 by Ba Khiet Le, Le, Ba Khiet · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Computational Techniques in Science and Engineering #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Mathematical Control Systems and Analysis #math.CA

paper · pdf · doi:10.48550/arxiv.1606.05197

arxiv created 2016/06/16 · arxiv updated 2016/06/17

Abstract

In this paper, some regularity properties of solutions of the following differential inclusion \ x(t) ∈ f(x(t)) -N_C(x(t)) \rm a.e. t ∈ [0,+∞), x(0) = x₀∈ C,. are analyzed where f: H→ H is Lipschitz continuous and C is closed, uniformly prox-regular subset of a Hilbet space H. Here N_C(⋅) denotes the proximal normal cone of C. This work can be considered as an improvement of [Hantoute-Mazade 2013] since these properties are established without the additional tangential condition at each point in C.

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