Modeling, analysis, and numerical approximations of the forced Fisher's equation and related control problems

Date
2002-01-01
Authors
Zhu, Wenxiang
Major Professor
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Max D. Gunzburger
L. Steven Hou
Committee Member
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Altmetrics
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Mathematics
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Mathematics
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.

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