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.