Reaction-Diffusion Systems with Discontinuous Reaction Functions

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Title: Reaction-Diffusion Systems with Discontinuous Reaction Functions
Author: He, Taiping
Advisors: C. V. Pao, Committee Chair
E. Chukwu, Committee Member
Z. Li, Committee Member
R. White, Committee Member
Abstract: This dissertation studies coupled reaction diffusion systems with discontinuous reaction functions. It includes three parts: The first part is concerned with the existence of solutions for a coupled system of two parabolic equations and the second part is devoted to the monotone iterative methods for monotone and mixed quasimonotone functions. Various monotone iterative schemes are presented and each of these schemes leads to an existence-comparison theorem and the monotone convergence of the maximal and minimal sequences. In the third part, the monotone iterative schemes are applied to compute numerical solutions of the system. These numerical solutions are based on the finite element method which gives a finite approximation of the coupled system. Numerical results for some scalar parabolic bounday problems and a coupled system of parabolic equations are also given.
Date: 2005-07-18
Degree: PhD
Discipline: Mathematics

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