PATH-FOLLOWING FOR DISJOINT BIFURCATION PROBLEMS ARISING IN IGNITION THEORY

The correct formulation governing the ignition of a solid reactant und ergoing slow oxidation gives rise to a nonlinear problem which in symm etrical geometries (infinite slab, cylinder, and sphere) is a two poin t boundary value problem. The discontinuity in the smallest branch of steady-states is the threshold for ignition. The solution branches are found by modifications of the path-following software (AUTO). Gross m ultiplicity of steady-states occurs for dimensions greater than two, a nd in all cases, the diagrams exhibit ''disjointedness'' for some para meter values which require special redefinition of the nonlinearity.