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Title:  Unfolding Operators in Various Oscillatory Domains : Homogenization of Optimal Control Problems 
Authors:  Aiyappan, S 
Advisors:  Nandakumaran, A K 
Keywords:  Unfolding Operators Oscillatory Domains Twoscale Convergence Biharmonic Equation Oscillating Boundary Domain Oscillating Domains Optimal Control Problem 
Submitted Date:  2017 
Series/Report no.:  G28585 
Abstract:  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 25. Chapter 6 presents the conclusions of the thesis and possible further directions. A brief description of our work (Chapters 25) 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 nonlinear elliptic problem is studied using this new unfolding 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 nonlinear optimal control problem posed on a smooth oscillating domain as in Figure 1(C) is studied using the unfolding operator. 
Abstract file URL:  http://etd.iisc.ernet.in/abstracts/4566/G28585Abs.pdf 
URI:  http://etd.iisc.ernet.in/2005/3696 
Appears in Collections:  Mathematics (math)

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