Bounds and critical parameters for a combustion problem

A model from combustion theory consisting of a nonlinear elliptic equation and boundary conditions of Dirichlet type, is considered. Upper and lower solutions for the problem are obtained by solving linear elliptic equations. These solutions are used to obtain analytical bounds for the extinction and ignition limits. Numerical results are presented for the slab, cylindrical and spherical geometries. Results compare very well with existing ones in the literature.