{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:30:34Z","timestamp":1787322634345,"version":"build-2736575974"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p>We study the relation between sweeping processes with the cone of limiting normals and projection processes. We prove the existence of a solution of a perturbed sweeping process with the cone of limiting normals and of nonstationary projection processes, provided the sets involved are definable (and are moving in a definable way) in some o-minimal structure. An application to a crowd motion model is presented.<\/jats:p>","DOI":"10.1137\/141000701","type":"journal-article","created":{"date-parts":[[2015,9,8]],"date-time":"2015-09-08T11:45:10Z","timestamp":1441712710000},"page":"2819-2834","source":"Crossref","is-referenced-by-count":1,"title":["Projection Process with Definable Right-Hand Side"],"prefix":"10.1137","volume":"53","author":[{"given":"Mira","family":"Bivas","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nadezhda","family":"Ribarska","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,9,8]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s11228-013-0230-y"},{"key":"atypb2","first-page":"451","volume":"17","author":"Bernicot F.","year":"2010","journal-title":"J. Convex Anal."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2010035"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.3934\/nhm.2007.2.313"},{"key":"atypb5","unstructured":"F. H. Clarke , Y. S. Ledyaev, R. J. Stern, and P. R. Wolenski,\n                      Nonsmooth Analysis and Control Theory\n                      , Springer-Verlag, New York, 1998."},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(83)90032-X"},{"key":"atypb7","doi-asserted-by":"crossref","unstructured":"M. Coste,\n                      An Introduction to O-Minimal Geometry\n                      , http:\/\/perso.univ-rennes1.fr\/michel.coste\/polyens\/OMIN.pdf (1999).","DOI":"10.1007\/978-3-662-03718-8_1"},{"key":"atypb8","doi-asserted-by":"crossref","unstructured":"L. Van den Dries,\n                      Tame Topology And O-Minimal Structures\n                      , Cambridge University Press, Cambridge, UK, 1998.","DOI":"10.1017\/CBO9780511525919"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-005-0619-y"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2005.12.005"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1007\/s11228-013-0257-0"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0531(72)90138-X"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(73)90192-3"},{"key":"atypb14","unstructured":"J. J. Moreau,\n                      Rafle par un convexe variable\n                      I, Se\u0301m. Anal. Convexe Montpellier, Expose\u0301 15, Univ. Sci. Tech. Languedoc, Montpellier, 1971."},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(77)90085-7"},{"key":"atypb16","first-page":"171","author":"Moreau J. J.","year":"1974","journal-title":"Rome"},{"key":"atypb17","unstructured":"R. T. Rockafellar and R. Wets,\n                      Variational Analysis\n                      , Grundlehren Math. Wiss. 317, Springer-Verlag, Berlin, 2004."},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012901395935"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0396(03)00129-3"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1007\/BF01027640"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/141000701","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:23:50Z","timestamp":1787318630000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/141000701"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1]]},"references-count":20,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2015,1]]}},"alternative-id":["10.1137\/141000701"],"URL":"https:\/\/doi.org\/10.1137\/141000701","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1]]}}}