{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T20:36:51Z","timestamp":1759091811685,"version":"3.37.3"},"reference-count":22,"publisher":"Walter de Gruyter GmbH","issue":"4","funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["SPP 1253"],"award-info":[{"award-number":["SPP 1253"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We consider an optimal control problem subject to the thin-film equation.\nThe PDE constraint lacks well-posedness for general right-hand sides due to possible degeneracies; state constraints are used to circumvent this problematic issue and to ensure well-posedness. Necessary optimality conditions for the optimal control problem are then derived. A convergent multi-parameter regularization is considered which addresses both, the possibly degenerate term in the equation and the state constraint. Some computational studies are then reported which evidence the relevant role of the state constraint, and motivate proper scalings of involved regularization and numerical parameters.<\/jats:p>","DOI":"10.1515\/cmam-2016-0025","type":"journal-article","created":{"date-parts":[[2016,9,22]],"date-time":"2016-09-22T12:56:36Z","timestamp":1474548996000},"page":"685-702","source":"Crossref","is-referenced-by-count":2,"title":["Optimal Control for the Thin Film Equation: Convergence of a Multi-Parameter Approach to Track State Constraints Avoiding Degeneracies"],"prefix":"10.1515","volume":"16","author":[{"given":"Markus","family":"Klein","sequence":"first","affiliation":[{"name":"Mathematisches Institut, Universit\u00e4t T\u00fcbingen, Auf der Morgenstelle 10, 72076 T\u00fcbingen, Germany"}]},{"given":"Andreas","family":"Prohl","sequence":"additional","affiliation":[{"name":"Mathematisches Institut, Universit\u00e4t T\u00fcbingen, Auf der Morgenstelle 10,72076 T\u00fcbingen, Germany"}]}],"member":"374","published-online":{"date-parts":[[2016,9,22]]},"reference":[{"key":"2023033116455891305_j_cmam-2016-0025_ref_001_w2aab3b7e2923b1b6b1ab2b1b1Aa","doi-asserted-by":"crossref","unstructured":"Abergel F. and Temam R.,\nOn some control problems in fluid mechanics,\nTheoret. Comput. Fluid Dyn. 1 (1990), no. 6, 303\u2013325.","DOI":"10.1007\/BF00271794"},{"key":"2023033116455891305_j_cmam-2016-0025_ref_002_w2aab3b7e2923b1b6b1ab2b1b2Aa","doi-asserted-by":"crossref","unstructured":"Alibert J.-J. and Raymond J.-P.,\nA Lagrange multiplier theorem for control problems with state constraints,\nNumer. Funct. Anal. Optim. 19 (1998), no. 7\u20138, 697\u2013704.","DOI":"10.1080\/01630569808816854"},{"key":"2023033116455891305_j_cmam-2016-0025_ref_003_w2aab3b7e2923b1b6b1ab2b1b3Aa","doi-asserted-by":"crossref","unstructured":"Becker J. and Gr\u00fcn G.,\nThe thin-film equation: Recent advances and some new perspectives,\nJ. Phys. 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