Abstract

Steady state solutions for spontaneous thermal ignition in a unit cube are considered. It is well known that for the unitsphere there are numerous solutions possible. These appear as ``wiggles" in the bifurcation diagram. For the unit sphere this can be shown analytically. In contrast for the unit cube analytic solutions are not possible hence we must resort to numerical methods to determine the corresponding bifurcation diagram. Some of the difficulties encountered using path following methods for this problem will be highlighted. Comparisons between the cube and the sphere are made.

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