Optimal Control of the Obstacle Problem in a Perforated Domain
2012 (English)In: Applied mathematics and optimization, ISSN 0095-4616, E-ISSN 1432-0606, Vol. 66, no 2, 239-255 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2012. Vol. 66, no 2, 239-255 p.
Optimal control, Perforated domains, Obstacle problem, Homogenization
IdentifiersURN: urn:nbn:se:uu:diva-268045DOI: 10.1007/s00245-012-9170-4ISI: 000308229100004ScopusID: 2-s2.0-84867278843OAI: oai:DiVA.org:uu-268045DiVA: diva2:875685