TY - JOUR
T1 - Upper and lower bounds for a reactive-diffuse system with Arrhenius kinetics
AU - Al-Refai, Mohammed
AU - Katatbeh, Qutaibeh
PY - 2006
Y1 - 2006
N2 - 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.
AB - 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.
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U2 - 10.1155/IJMMS/2006/24391
DO - 10.1155/IJMMS/2006/24391
M3 - Article
AN - SCOPUS:33749505848
SN - 0161-1712
VL - 2006
JO - International Journal of Mathematics and Mathematical Sciences
JF - International Journal of Mathematics and Mathematical Sciences
M1 - 24391
ER -