{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:20:25Z","timestamp":1787322025675,"version":"build-2736575974"},"reference-count":28,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p>In this paper, we investigate optimal boundary control problems for Cahn--Hilliard variational inequalities with a dynamic boundary condition involving double obstacle potentials and the Laplace--Beltrami operator. The cost functional is of standard tracking type, and box constraints for the controls are prescribed. We prove existence of optimal controls and derive first-order necessary conditions of optimality. The general strategy, which follows the lines of the recent approach by Colli, Farshbaf-Shaker, and Sprekels [Appl. Math. Optim., 71 (2015), pp. 1--24] to the (simpler) Allen--Cahn case, is the following: we use the results that were recently established by Colli, Gilardi, and Sprekels [Appl. Math. Optim., Online First DOI:10.1007\/s00245-015-9299-z, 2015] for the case of (differentiable) logarithmic potentials and perform a so-called deep quench limit. Using compactness and monotonicity arguments, it is shown that this strategy leads to the desired first-order necessary optimality conditions for the case of (nondifferentiable) double obstacle potentials.<\/jats:p>","DOI":"10.1137\/140984749","type":"journal-article","created":{"date-parts":[[2015,8,27]],"date-time":"2015-08-27T12:46:31Z","timestamp":1440679591000},"page":"2696-2721","source":"Crossref","is-referenced-by-count":50,"title":["Optimal Boundary Control of a Viscous Cahn--Hilliard System with Dynamic Boundary Condition and Double Obstacle Potentials"],"prefix":"10.1137","volume":"53","author":[{"given":"Pierluigi","family":"Colli","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M. Hassan","family":"Farshbaf-Shaker","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gianni","family":"Gilardi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00fcrgen","family":"Sprekels","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,8,27]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/8\/2\/002"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(81)90125-6"},{"key":"atypb3","unstructured":"H. Brezis,\n                      Ope\u0301rateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert\n                      , North-Holland Math. Stud. 5, North-Holland, Amsterdam, 1973."},{"key":"atypb4","unstructured":"F. Brezzi and G. Gilardi,\n                      Finite Element Handbook\n                      , H. Kardestuncer and D. H. Norrie, eds., McGraw-Hill, New York, 1987."},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2012.11.010"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2008.03.020"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-014-9250-8"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/s00161-011-0215-8"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/s00032-012-0181-z"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2014.05.008"},{"key":"atypb11","doi-asserted-by":"publisher","unstructured":"P. Colli, G. Gilardi, and J. Sprekels,\n                      A boundary control problem for the viscous Cahn-Hilliard equation with dynamic boundary conditions\n                      , Appl. Math. Optim., Online First DOI:10.1007\/s00245-015-9299-z, 2015.","DOI":"10.1007\/s00245-015-9299-z,"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/120902422"},{"key":"atypb13","first-page":"1","volume":"887","author":"Elliott C. M.","year":"1991","journal-title":"IMA Preprints Series"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1080\/01630563.2012.672354"},{"key":"atypb15","doi-asserted-by":"publisher","unstructured":"M. H. Farshbaf-Shaker,\n                      A relaxation approach to vector-valued Allen-Cahn MPEC problems\n                      , Appl. Math. Optim., Online First DOI:10.1007\/s00245-014-9282-0, 2014.","DOI":"10.1007\/s00245-014-9282-0,"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.3934\/cpaa.2009.8.881"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/s11401-010-0602-7"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-99-02445-9"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1137\/110824152"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/120865628"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-36062-6_35"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1007\/s11587-006-0008-8"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1137\/140964308"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/BF01762360"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2014.02.006"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2011.06.015"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1080\/00036811.2011.643786"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-013-9234-0"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/140984749","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:17:14Z","timestamp":1787318234000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/140984749"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1]]},"references-count":28,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2015,1]]}},"alternative-id":["10.1137\/140984749"],"URL":"https:\/\/doi.org\/10.1137\/140984749","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1]]}}}