Degree Type

Dissertation

Date of Award

2003

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Max D. Gunzburger

Second Advisor

L. Steven Hou

Abstract

Terminal-state tracking optimal control problems for linear and semilinear parabolic equations are studied. The control objective is to track a desired terminal state and the control is of the distributed type. A distinctive feature of this work is that the controlled state and the target state are allowed to have nonmatching boundary conditions.;In the linear case, analytic solution formulae for the optimal control problems are derived in the form of eigen series. Pointwise-in-time L2 norm estimates for the optimal solutions are obtained and approximate controllability results are established. Exact controllability is shown when the target state and the controlled state have matching boundary conditions. One-dimensional computational results are presented which illustrate the terminal-state tracking properties for the solutions expressed by the series formulae.;In the semilinear case, the existence of an optimal control solution is shown. The dynamics of the optimal control solution is analyzed. Error estimates are obtained for semidiscrete (spatially discrete) approximations of the optimal control problem in two and three space dimensions. A gradient algorithm is discussed and numerical results are presented.

DOI

https://doi.org/10.31274/rtd-180813-11127

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu

Copyright Owner

Hee-Dae Kwon

Language

en

Proquest ID

AAI3105082

File Format

application/pdf

File Size

61 pages

Included in

Mathematics Commons

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