Degree Type

Dissertation

Date of Award

2002

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Max D. Gunzburger

Second Advisor

L. Steven Hou

Abstract

The Fisher equation with inhomogeneous forcing is considered in this work. First, a forced Fisher equation and boundary conditions are derived. Then, the existence of a local and global solution for the forced equation with a homogeneous Dirichlet condition is proved and the results are generalized to the case of less regular forces. Semi-discrete finite element approximations, semi-discrete approximations in the time variable, and fully discrete approximations are studied under certain minimal regularity assumptions. Numerical experiments are carried out and computational results are presented. An optimal distributed control problem related to the forced Fisher equation is also considered, the optimality system is derived, and numerical approximations of the optimality system are discussed.

DOI

https://doi.org/10.31274/rtd-180813-13144

Publisher

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

Copyright Owner

Wenxiang Zhu

Language

en

Proquest ID

AAI3061880

File Format

application/pdf

File Size

125 pages

Included in

Mathematics Commons

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