Abstract

This paper addresses the Cauchy problem for the quasi-variational sweeping process in the ordered Hilbert space HH −u′(t)∈NC(t,u(t))(u(t))for a.e. t∈(0,T),u(0)=u0,-u^{\prime}(t) \in N_{C(t,u(t))}(u(t)) \quad \text{for a.e. } t \in (0,T), \quad u(0)=u_0, where the set  C(t,u(t))⊂H \, C(t,u(t)) \subset H \, is non-convex and  NC(t,u(t)) \, N_{C(t,u(t))} \, denotes its normal cone. We provide an existence result based on the classical implicit time-discretization procedure and on a fixed point argument in ordered spaces.

Author information

Contact details are reproduced from the original publication and may be historical.

Nikolai V. Chemetov

Universidade de Lisboa, Faculdade de Ciências, Dep. de Matemática, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal

chemetov@ptmat.fc.ul.pt

Manuel D. P. Monteiro Marques

Universidade de Lisboa, Faculdade de Ciências, Dep. de Matemática, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal

mmarques@ptmat.fc.ul.pt

Keywords

  • Sweeping process
  • non-convex sets
  • orders in Hilbert spaces

Mathematics Subject Classification

34A60, 34G25, 47J20

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Suggested citation

N. V. Chemetov, M. D. P. Monteiro Marques, U. Stefanelli. “Ordered Non-Convex Quasi-Variational Sweeping Processes.” Journal of Convex Analysis 15 (2008), No. 2, 201–214. https://doi.org/10.68381/jca15014

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Published by Heldermann Verlag, 2008. Rights now held by Banach Press LLC.