Geodesic
Ordered Non-Convex Quasi-Variational Sweeping Processes
Journal of convex analysis, Tome 15 (2008) no. 2, pp. 201-214.

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 34A60, 34G25, 47J20
Mots-clés : Sweeping process, non-convex sets, orders in Hilbert spaces 
@article{JCA_2008_15_2_JCA_2008_15_2_a0,
     author = {N. V. Chemetov and M. D. P. Monteiro Marques and U. Stefanelli},
     title = {Ordered {Non-Convex} {Quasi-Variational} {Sweeping} {Processes}},
     journal = {Journal of convex analysis},
     pages = {201--214},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2008},
     url = {http://geodesic.mathdoc.fr/item/JCA_2008_15_2_JCA_2008_15_2_a0/}
}
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N. V. Chemetov; M. D. P. Monteiro Marques; U. Stefanelli. Ordered Non-Convex Quasi-Variational Sweeping Processes. Journal of convex analysis, Tome 15 (2008) no. 2, pp. 201-214. http://geodesic.mathdoc.fr/item/JCA_2008_15_2_JCA_2008_15_2_a0/