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Unfolding Operators in Various Oscillatory Domains : Homogenization of Optimal Control Problems

Electronic Theses of Indian Institute of Science

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Title Unfolding Operators in Various Oscillatory Domains : Homogenization of Optimal Control Problems
 
Creator Aiyappan, S
 
Subject Unfolding Operators
Oscillatory Domains
Two-scale Convergence
Biharmonic Equation
Oscillating Boundary Domain
Oscillating Domains
Optimal Control Problem
Mathematics
 
Description In this thesis, we study homogenization of optimal control problems in various oscillatory domains. Specifically, we consider four types of domains given in Figure 1 below.
Figure 1: Oscillating Domains
The thesis is organized into six chapters. Chapter 1 provides an introduction to our work and the rest of the thesis. The main contributions of the thesis are contained in Chapters 2-5. Chapter 6 presents the conclusions of the thesis and possible further directions. A brief description of our work (Chapters 2-5) follows:
Chapter 2: Asymptotic behaviour of a fourth order boundary optimal control problem with Dirichlet boundary data posed on an oscillating domain as in Figure 1(A) is analyzed. We use the unfolding operator to study the asymptotic behavior of this problem.
Chapter 3: Homogenization of a time dependent interior optimal control problem on a branched structure domain as in Figure 1(B) is studied. Here we pose control on the oscillating interior part of the domain. The analysis is carried out by appropriately defined unfolding operators suitable for this domain. The optimal control is characterized using various unfolding operators defined at each branch of every level.
Chapter 4: A new unfolding operator is developed for a general oscillating domain as in Figure 1(C). Homogenization of a non-linear elliptic problem is studied using this new un-folding operator. Using this idea, homogenization of an optimal control problem on a circular oscillating domain as in Figure 1(D) is analyzed.
Chapter 5: Homogenization of a non-linear optimal control problem posed on a smooth oscillating domain as in Figure 1(C) is studied using the unfolding operator.
 
Contributor Nandakumaran, A K
 
Date 2018-06-13T07:46:45Z
2018-06-13T07:46:45Z
2018-06-13
2017
 
Type Thesis
 
Identifier http://etd.iisc.ernet.in/2005/3696
http://etd.iisc.ernet.in/abstracts/4566/G28585-Abs.pdf
 
Language en_US
 
Relation G28585