{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:46:29Z","timestamp":1787319989379,"version":"build-2736575974"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>We consider a control- and state-constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions occur during the modeling of diffuse-gray conductive-radiative heat transfer. The nonlocal radiation interface condition and the pointwise state constraints represent the particular features of this problem. To deal with the state constraints, continuity of the state is shown, which allows us to derive first-order necessary conditions. Afterwards, we establish second-order sufficient conditions that account for strongly active sets and ensure local optimality in an $L^2$-neighborhood.<\/jats:p>","DOI":"10.1137\/070694788","type":"journal-article","created":{"date-parts":[[2009,2,20]],"date-time":"2009-02-20T18:24:14Z","timestamp":1235154254000},"page":"734-755","source":"Crossref","is-referenced-by-count":11,"title":["State-Constrained Optimal Control of Semilinear Elliptic Equations with Nonlocal Radiation Interface Conditions"],"prefix":"10.1137","volume":"48","author":[{"given":"C.","family":"Meyer","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"I.","family":"Yousept","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,2,20]]},"reference":[{"key":"R1","unstructured":"R. A. Adams,\n                      Sobolev Spaces\n                      , Pure Appl. 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Meyer,\n                      An SQP active set method for a semilinear optimal control problem with nonlocal radiation interface conditions\n                      , in Control of Coupled Partial Differential Equations, K. Kunisch, G. Leugering, F. Tr\u00f6ltzsch, and J. Sprekels, eds., Internat. Ser. Numer. Math. 155, Birkh\u00e4user Basel, 2007, pp. 217\u2013248.","DOI":"10.1007\/978-3-7643-7721-2_10"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1051\/cocv:2007028"},{"key":"R19","unstructured":"P. Philip,\n                      Transient Numerical Simulation of Sublimation Growth of SiC Bulk Single Crystals. Modeling, Finite Volume Method, Results\n                      , Ph.D. thesis, Department of Mathematics, Humboldt University of Berlin, Berlin, 2003."},{"key":"R20","first-page":"385","volume":"18","author":"Serrin J.","year":"1964","journal-title":"Ann. Scuola Norm. Sup. 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Zeidler,\n                      Nonlinear Functional Analysis and Its Application\n                      II\n                      \/B: Nonlinear Monotone Operators\n                      , Springer, New York, 1990.","DOI":"10.1007\/978-1-4612-0981-2"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/070694788","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:54:29Z","timestamp":1787316869000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/070694788"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1137\/070694788"],"URL":"https:\/\/doi.org\/10.1137\/070694788","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}