Sweeping processes are a class of evolution differential inclusions arising in elastoplasticity and were introduced by J.J. Moreau in the early seventies. The solution operator of the sweeping processes represents a relevant example of rate independent operator. As a particular case we get the so called play operator, which is a typical example of a hysteresis operator. The continuity properties of these operators were studied in several works. In this paper we address the continuity with respect to the strict metric in the space of functions of bounded variation with values in the metric space of closed convex subsets of a Hilbert space. We provide counterexamples showing that for all BV-formulations of the sweeping process the corresponding solution operator is not continuous when its domain is endowed with the strict topology of BV and its codomain is endowed with the L1 topology. This is at variance with the play operator which has a BV-extension that is continuous in this case.

Hausdorff metric BV discontinuity of sweeping processes / Klein, O.; Recupero, Vincenzo. - In: JOURNAL OF PHYSICS. CONFERENCE SERIES. - ISSN 1742-6588. - STAMPA. - 727:1(2016), pp. 1-12. [10.1088/1742-6596/727/1/012006]

Hausdorff metric BV discontinuity of sweeping processes

RECUPERO, VINCENZO
2016

Abstract

Sweeping processes are a class of evolution differential inclusions arising in elastoplasticity and were introduced by J.J. Moreau in the early seventies. The solution operator of the sweeping processes represents a relevant example of rate independent operator. As a particular case we get the so called play operator, which is a typical example of a hysteresis operator. The continuity properties of these operators were studied in several works. In this paper we address the continuity with respect to the strict metric in the space of functions of bounded variation with values in the metric space of closed convex subsets of a Hilbert space. We provide counterexamples showing that for all BV-formulations of the sweeping process the corresponding solution operator is not continuous when its domain is endowed with the strict topology of BV and its codomain is endowed with the L1 topology. This is at variance with the play operator which has a BV-extension that is continuous in this case.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2611357
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