Upper and lower bounds for a reactive-diffuse system with Arrhenius kinetics - Mohammed Al-Refai; Qutaibeh Katatbeh (International Journal of Mathematics and Mathematical Sciences)
Comparison arguments are used to study a problem in combustion theory consisting of a nonlinear parabolic equation together with initial and boundary conditions. Upper and lower bounds for the problem are constructed. The lower solutions are used to determine whether the solution of the problem is increasing in time for certain initial condition. Numerical results are presented for the slab, infinite cylinder, and unit sphere. The bounds are compared with the existing ones in the literature for the slab geometry.