On the existence and uniqueness result for a two-step reactive-diffusive equation with variable pre-exponential factor

Abstract

We examine the existence and uniqueness result of the steady-state solutions for the exothermic chemical reactions taking the diffusion of the reactants in a slab into account and assuming Arrhenius dependence with variable pre-exponential factor. We establish the criteria\'s and conditions for existence and uniqueness of solution for the newly formulated problem. It is shown that if Γ>o, 0≤x₁𕟩, 0≤x₂≤b and -c≤x₃≤C where b, c and C positive constants are then the newly formulated model will have only one solution. We further discovered that there are certain values for n, m, r and β that the problem can accommodate for solution to be stable. Similarly, Frank-Kamenetskii parameters ┉, ┊ must not exceed some values for the solution to exist and at the same time stable. Finally, the Frank-Kamenetskii parameter must not exceed the critical value for the solution to have physical implication or application and r must not be large for convergence of the solution (i.e r < 1).

Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 403-408