Existence of Solutions to the Nonconvex Sweeping Process

✍ Scribed by Houcine Benabdellah

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 133 KB
• Volume: 164
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1999.3756

✦ Synopsis

In this note, we prove the existence of solutions for the sweeping process problem x$(t) # &N C(t) (x(t)) a.e., x(t) # C(t), x(0)=x 0 # C(0), where C(.) is an arbitrary Hausdorff Lipschitzean multifunction, from I=[0, T] onto the set of nonempty closed subsets of R d . This generalizes a well known result of J. J. Moreau, (1971, in ``Sem. d'Analyse Convexe, Montpelier,'' Exp. 15) in the convex case. 2000