Abstract

Inverse problems of parameter identification and source identification in partial differential equations are highly ill-posed problems and for their satisfactory theoretical and numerical treatment some sort of regularization is necessary. In this thesis, we pose this inverse problem as an optimization problem and perform the regularization in Tikhonov sense. The most crucial aspect of the study of the regularized optimization problem is a proper selection of the regularization parameter. Although the theory for one of the most efficient methods for choosing an optimal regularization parameter, the so-called Morozov discrepancy principle, is well-developed for linear inverse problems, its use for nonlinear inverse problems is rather heuristic. In this thesis, we investigate the inverse problem of parameter identification using an equation error approach in which the coefficient appear linearly. Using the results known for linear inverse problems, we develop a rigorous Morozov discrepancy principle for nonlinear inverse problems. We present a detailed computational experimentation to test the feasibility of the developed approach. We also study the inverse problem of source identification in fourth-order boundary value problem.

Library of Congress Subject Headings

Inverse prob lems (Differential equations); Mathematical optimization

Publication Date

11-20-2015

Document Type

Thesis

Student Type

Graduate

Degree Name

Applied and Computational Mathematics (MS)

Department, Program, or Center

School of Mathematical Sciences (COS)

Advisor

Akhtar Khan

Advisor/Committee Member

Baasansuren Jadamba

Advisor/Committee Member

Patricia Clark

Comments

Physical copy available from RIT's Wallace Library at QA377 .C39 2015

Campus

RIT – Main Campus

Plan Codes

ACMTH-MS

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