Optimal Control of the Obstacle Problem in a Perforated Domain

Optimal Control of the Obstacle Problem in a Perforated Domain We study the problem of optimally controlling the solution of the obstacle problem in a domain perforated by small periodically distributed holes. The solution is controlled by the choice of a perforated obstacle which is to be chosen in such a fashion that the solution is close to a given profile and the obstacle is not too irregular. We prove existence, uniqueness and stability of an optimal obstacle and derive necessary and sufficient conditions for optimality. When the number of holes increase indefinitely we determine the limit of the sequence of optimal obstacles and solutions. This limit depends strongly on the rate at which the size of the holes shrink. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Optimal Control of the Obstacle Problem in a Perforated Domain

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Publisher
Springer-Verlag
Copyright
Copyright © 2012 by Springer Science+Business Media, LLC
Subject
Mathematics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-012-9170-4
Publisher site
See Article on Publisher Site

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