Journal of Convex Analysis 15 (2008), No. 2, 201--214
Copyright Heldermann Verlag 2008
Ordered Non-Convex Quasi-Variational Sweeping Processes
Nikolai V. Chemetov
Universidade de Lisboa, Faculdade de Ciencias, 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 Ciencias, Dep. de Matemática, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal
mmarques@ptmat.fc.ul.pt
Ulisse Stefanelli
Università di Pavia, Ist. di Matematica Applicata e Tecnologie Informatiche, Via Ferrata 1, 27100 Pavia, Italy
ulisse.stefanelli@imati.cnr.it
[Abstract-pdf]
This paper addresses the Cauchy problem for the quasi-variational sweeping process in the ordered Hilbert space $H$ \begin{equation*} -u^{\prime}(t) \in N_{C(t,u(t))}(u(t)) \quad \text{for a.e. $\, t \in (0,T),$% } \ \ u(0)=u_0, \end{equation*} where the set $\, C(t,u(t)) \subset H \,$ is non-convex and $\, N_{C(t,u(t))} \,$ 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.
Keywords: Sweeping process, non-convex sets, orders in Hilbert spaces.
MSC: 34A60, 34G25, 47J20
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