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
Copyright Date
2002
Language
en
Proquest ID
AAI3061880
File Format
application/pdf
File Size
125 pages
Recommended Citation
Zhu, Wenxiang, "Modeling, analysis, and numerical approximations of the forced Fisher's equation and related control problems " (2002). Retrospective Theses and Dissertations. 495.
https://lib.dr.iastate.edu/rtd/495
