2014
DOI: 10.1007/s10107-014-0754-4
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Convex sweeping process in the framework of measure differential inclusions and evolution variational inequalities

Abstract: International audienceIn this paper, we analyze and discuss the well-posedness of two new variants of the so-called sweeping process, introduced by Moreau in the early 70s with motivation in plasticity theory. The first new variant is concerned with the perturbation of the normal cone to the moving convex subset $C(t)$, supposed to have a bounded variation, by a Lipschitz mapping. Under some assumptions on the data, we show that the perturbed differential measure inclusion has one and only one right continuous… Show more

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Cited by 85 publications
(102 citation statements)
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“…Most of the results can be found in [1,11]. For the convenience of the reader, we recall them in this part of the paper.…”
Section: Radon Measurementioning
confidence: 99%
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“…Most of the results can be found in [1,11]. For the convenience of the reader, we recall them in this part of the paper.…”
Section: Radon Measurementioning
confidence: 99%
“…As in [1], the concept of solution does not depend on the measure ν in the sense that a mapping u(·) : I −→ H satisfying (a) above is a solution of P if and only if (b) and (c) hold for any positive Radon measure ν which is absolutely continuously equivalent to μ + λ. Indeed, let u(·) : I −→ H be a solution of P and let ν 0 , given by the definition of a solution to P, be an associated Radon measure absolutely continuously equivalent to μ + λ for which du…”
Section: D(y C(s)) − D(y C(t))| ≤ μ(]S T]) For All S T ∈ I With mentioning
confidence: 99%
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“…[5][6][7][8][9][10]). In this paper, we are interested in a variant of sweeping processes associated with maximal monotone operators of following form ⎧ ⎨ ⎩ẋ (t) ∈−Ax(t) − N C(t) (x(t)) a.e.…”
Section: Introductionmentioning
confidence: 99%