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Computational Methods in Applied Mathematics

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Volume 16, Issue 4


Optimal Control for the Thin Film Equation: Convergence of a Multi-Parameter Approach to Track State Constraints Avoiding Degeneracies

Markus Klein / Andreas Prohl
  • Corresponding author
  • Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10,72076 Tübingen, Germany
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Published Online: 2016-09-22 | DOI: https://doi.org/10.1515/cmam-2016-0025


We consider an optimal control problem subject to the thin-film equation. The 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.

Keywords: Thin-Film Equation; Optimality Conditions; Penalty Approach; Optimal Control of Degenerate Equation

MSC 2010: 35K55; 35K65; 93C20; 93C95; 76A20


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About the article

Received: 2016-05-29

Revised: 2016-06-23

Accepted: 2016-08-03

Published Online: 2016-09-22

Published in Print: 2016-10-01

Funding Source: Deutsche Forschungsgemeinschaft

Award identifier / Grant number: SPP 1253

The work supported by a DFG grant within the Priority Program SPP 1253 (Optimization with Partial Differential Equations). This work was performed on the computational resource bwUniCluster funded by the Ministry of Science, Research and Arts and the Universities of the State of Baden-Württemberg, Germany, within the framework program bwHPC; cf. [bwGRiD, Member of the German D-Grid initiative, funded by the Ministry of Education and Research (Bundesministerium für Bildung und Forschung) and the Ministry for Science, Research and Arts Baden-Württemberg (Ministerium für Wissenschaft, Forschung und Kunst Baden-Württemberg), technical report, Universities of Baden-Württemberg, 2007–2010, www.bw-grid.de].

Citation Information: Computational Methods in Applied Mathematics, Volume 16, Issue 4, Pages 685–702, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2016-0025.

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