The thermal ignition problem in a cube

Abstract

Steady state solutions for spontaneous thermal ignition in a unit cube are considered. For the unit sphere there are numerous solutions possible: these appear as ``wiggles'' in the bifurcation diagram. For the unit sphere this has been shown analytically. In contrast, for the unit cube analytic solutions are not possible and hence we must resort to numerical methods to determine the corresponding bifurcation diagram. Comparisons between the cube and the sphere are made.