Degree Type

Dissertation

Date of Award

2012

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Steven L. Hou

Abstract

In this thesis, we mainly study the numerical methods for stochastic homogenization of elliptic optimal control problem, where there is random variable involved in the constraint. We start with a simple one-dimensional optimal control problem and derive the effective equations of the original optimal control problem and the theory results regarding the convergence of solutions have been studied in \cite{kesavan}. Then an elliptic optimal control problem with coefficient having ergodicity is studied and convergence theorem is also given regarding the effective equations. Finally, another elliptic optimal control problem, where the normal product is replaced by the wick product, is discussed. An algorithm used to search the optimal solution is obtained. Numerical examples are given in each chapter.

DOI

https://doi.org/10.31274/etd-180810-417

Copyright Owner

Zhen Li

Language

en

File Format

application/pdf

File Size

63 pages

Included in

Mathematics Commons

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