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Asymptotic analysis of Neumann periodic optimal boundary control problem
Author(s) -
Nandakumaran Akambadath,
Prakash Ravi,
Sardar Bidhan Chandra
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3865
Subject(s) - mathematics , homogenization (climate) , limiting , scaling , boundary (topology) , neumann boundary condition , optimal control , boundary value problem , mathematical analysis , limit (mathematics) , operator (biology) , scaling limit , mixed boundary condition , mathematical optimization , geometry , mechanical engineering , biodiversity , ecology , biochemistry , chemistry , repressor , gene , transcription factor , engineering , biology
An optimal boundary control problem in a domain with oscillating boundary has been investigated in this paper. The controls are acting periodically on the oscillating boundary. The controls are applied with suitable scaling parameters. One of the major contribution is the representation of the optimal control using the unfolding operator. We then study the limiting analysis (homogenization) and obtain two limit problems according to the scaling parameters. Another notable observation is that the limit optimal control problem has three controls, namely, a distributed control, a boundary control, and an interface control. Copyright © 2016 John Wiley & Sons, Ltd.