### Abstract

This paper is concerned with two mathematical models which describe the transient behavior of a catalytic converter in automobile engineering. The first model consists of a coupled system of a heat-conduction equation and two integral equations while the second model involves only one integral equation. It is shown that for any nonnegative initial and boundary functions the three-equation model has a unique bounded global solution while the solution of the two-equation model blows up in finite time. The proof for the global existence and finite-time blow-up property of the solution is by the method of upper and lower solutions and its associated monotone iteration. This method can be used to develop computational algorithms for numerical solutions of the coupled systems.

Original language | English |
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Pages (from-to) | 2152-2165 |

Number of pages | 14 |

Journal | Nonlinear Analysis: Real World Applications |

Volume | 14 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2013 Dec 1 |

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### ASJC Scopus subject areas

- Analysis
- Engineering(all)
- Economics, Econometrics and Finance(all)
- Computational Mathematics
- Applied Mathematics

### Cite this

*Nonlinear Analysis: Real World Applications*,

*14*(6), 2152-2165. https://doi.org/10.1016/j.nonrwa.2013.04.004