Kragujevac J. Math. 24 (2002) 61-71.
THE EFFECT OF A SPATIAL VARIABLE ON THE CRITICALITY OF A BOUNDARY VALUE PROBLEM
S. O. Ajadi
Department of Mathematics, Obafemi Awolowo University Ile-Ife, Nigeria.
(e-mail: sajadi@oauife.edu.ng)
Abstract.
The aim of this work is to investigate the effect of the function, f(x) > 0 on the
boundary value problem
for some f(x) > 0.
We established that there exist a dcr > 0, such that if
0 £ d £ dcr, a steady state solution for the boundary value problem exist,
while for d > dcr, no solution exist. Analytical solutions were obtained for some
f(x) > 0 and geometry, while a numerical method is applied to others where analytical method fails.
In particular, the variational method was implemented using the Mathematica software package.
These solutions have thus given us the choice of comparing the behaviour of the solutions for
the special cases of slab and cylinder. Our results have not only confirmed previous, it has
has facilitated a better understanding of the problem not previously considered.