### 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

**On a coupled system of reaction-diffusion-transport equations arising from catalytic converter.** / Pao, C. V.; Chang, Yu-Hsien; Jau, Guo Chin.

Research output: Contribution to journal › Article

*Nonlinear Analysis: Real World Applications*, vol. 14, no. 6, pp. 2152-2165. https://doi.org/10.1016/j.nonrwa.2013.04.004

}

TY - JOUR

T1 - On a coupled system of reaction-diffusion-transport equations arising from catalytic converter

AU - Pao, C. V.

AU - Chang, Yu-Hsien

AU - Jau, Guo Chin

PY - 2013/12/1

Y1 - 2013/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84878799820&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84878799820&partnerID=8YFLogxK

U2 - 10.1016/j.nonrwa.2013.04.004

DO - 10.1016/j.nonrwa.2013.04.004

M3 - Article

AN - SCOPUS:84878799820

VL - 14

SP - 2152

EP - 2165

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

SN - 1468-1218

IS - 6

ER -