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Title: Analysis of complex nonlinear reaction-diffusion equations
Author: Al-Ofl, Abdalaziz Saleem
ISNI:       0000 0001 3407 724X
Awarding Body: Durham University
Current Institution: Durham University
Date of Award: 2008
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A mathematical analysis has been carried out for some nonlinear reaction- diffusion equations on open bounded convex domains Ω C R(^d)(d < 3) with Robin boundary conditions- Existence, uniqueness and continuous dependence on initial data of weak and strong solutions are proved. A numerical analysis has also been undertaken for these nonlinear reaction- diffusion equations on the above domains. A fully practical piecewise linear finite element approximation is proposed for which existence and uniqueness of the numerical solution are proved. Semi-discrete and fully discrete error estimates are given. A practical algorithm for computing the numerical solution is given and its convergence is proved. Finally, some numerical simulations in one-dimensional space are exhibited.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available