### 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 |
---|---|

Pages (from-to) | 9-15 |

Number of pages | 7 |

Journal | Mathematical and Computer Modelling |

Volume | 19 |

Issue number | 9 |

DOIs | |

Publication status | Published - 1994 |

### Fingerprint

### 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

### Cite this

*Mathematical and Computer Modelling*,

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

**Path-following for disjoint bifurcation problems arising in ignition theory.** / Balakrishnan, E.; Swift, A.; Wake, G. C.

Research output: Contribution to journal › Article

*Mathematical and Computer Modelling*, vol. 19, no. 9, pp. 9-15. https://doi.org/10.1016/0895-7177(94)90036-1

}

TY - JOUR

T1 - Path-following for disjoint bifurcation problems arising in ignition theory

AU - Balakrishnan, E.

AU - Swift, A.

AU - Wake, G. C.

PY - 1994

Y1 - 1994

N2 - 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.

AB - 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.

KW - Combustion

KW - Limit points

KW - Nonlinear systems

KW - Numerics

UR - http://www.scopus.com/inward/record.url?scp=38149147232&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38149147232&partnerID=8YFLogxK

U2 - 10.1016/0895-7177(94)90036-1

DO - 10.1016/0895-7177(94)90036-1

M3 - Article

AN - SCOPUS:38149147232

VL - 19

SP - 9

EP - 15

JO - Mathematical and Computer Modelling

JF - Mathematical and Computer Modelling

SN - 0895-7177

IS - 9

ER -