Optimal Control for the Thin Film Equation: Convergence of a Multi-Parameter Approach to Track State Constraints Avoiding Degeneracies
2016 ◽
Vol 16
(4)
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pp. 685-702
Keyword(s):
AbstractWe 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.
2015 ◽
Vol 64
(4)
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pp. 623-647
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2011 ◽
Vol 69
(3)
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pp. 534-549
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2007 ◽
Vol 87
(8-9)
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pp. 564-589
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2018 ◽
Vol 52
(5)
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pp. 1617-1650
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1979 ◽
Vol 20
(2)
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pp. 301-312
Keyword(s):
2014 ◽
Vol 2014
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pp. 1-9
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