Path-following for disjoint bifurcation problems arising in ignition theory

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Abstract

The correct formulation governing the ignition of a solid reactant undergoing slow oxidation gives rise to a nonlinear problem which in symmetrical geometries (infinite slab, cylinder, and sphere) is a two point 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 multiplicity of steady-states occurs for dimensions greater than two, and in all cases, the diagrams exhibit “disjointedness” for some parameter values which require special redefinition of the nonlinearity.

Keywords

Nonlinear systems
Combustion
Limit points
Numerics

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