Homogenization in Perforated Domains
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Homogenization theory is the study of the asymptotic behaviour of solutionsto partial differential equations where high frequency oscillations occur.In the case of a perforated domain the oscillations are due to variations in thedomain of the equation. The four articles that constitute this thesis are devotedto obstacle problems in perforated domains. Paper A treats an optimalcontrol problem where the objective is to control the solution to the obstacleproblem by the choice of obstacle. The optimal obstacle in the perforated domain,as well as its homogenized limit, are characterized in terms of certainauxiliary problems they solve. In papers B,C and D the authors solve homogenizationproblems in a perforated domain where the perforation is definedas the intersection between a periodic perforation and a hyper plane. Thetheory of uniform distribution is an indespensible tool in the analysis of theseproblems. Paper B treats the obstacle problem for the Laplace operator andthe authors use correctors to derive a homogenized equation. Paper D is ageneralization of paper B to the p-Laplacian. The authors employ capacitytechniques which are well adapted to the problem. In Paper C the obstaclevaries on the same scale as the perforations. In this setting the authorsemploy the theory of Gamma-convergence to prove a homogenization result.
Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. , vii, 22 p.
Research subject Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-147702ISBN: 978-91-7595-213-0OAI: oai:DiVA.org:kth-147702DiVA: diva2:731865
2014-09-05, F3, Lindstedtsvägen 25, KTH, Stockholm, 13:00 (English)
Armstrong, Scott, Chargé de Recherge
Shahgholian, Henrik, Professor
QC 201407032014-07-032014-07-022014-07-03Bibliographically approved
List of papers