### 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.

Original language | English |
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Pages (from-to) | 9-15 |

Number of pages | 7 |

Journal | Mathematical and Computer Modelling |

Volume | 19 |

Issue number | 9 |

DOIs | |

Publication status | Published - 1994 |

### Keywords

- Combustion
- Limit points
- Nonlinear systems
- Numerics

### ASJC Scopus subject areas

- Computer Science (miscellaneous)
- Information Systems and Management
- Control and Systems Engineering
- Applied Mathematics
- Computational Mathematics
- Modelling and Simulation

## Fingerprint Dive into the research topics of 'Path-following for disjoint bifurcation problems arising in ignition theory'. Together they form a unique fingerprint.

## Cite this

Balakrishnan, E., Swift, A., & Wake, G. C. (1994). Path-following for disjoint bifurcation problems arising in ignition theory.

*Mathematical and Computer Modelling*,*19*(9), 9-15. https://doi.org/10.1016/0895-7177(94)90036-1