### Abstract

The main purpose of this paper is to study the thermal balance equations for the gas and solid interphase heat-transfer for the fast-igniting catalytic converter of automobiles: { ∂/∂t u (t, x) = - α∂/∂x u (t, x) + av (t, x) - au (t, x) for t > 0, 0 < x < l; ∂/∂t v (t, x) = bu (t, x) - bv (t, x) + λexp (v (t, x)) for t > 0, 0 < x < l; u (t, 0) = η for t ≥ 0; u (0, x) = u_{0} (x) and v (0, x) = v_{0} (x) for x > 0. where u_{0}, v_{0} are continuous functions on [0, l] with u_{0} (0) = η. We establish some results concerning the existence and uniqueness of the mild solutions and classical solutions of the above differential system. The asymptotical behavior of the solution is also addressed.

Original language | English |
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Pages (from-to) | 807-827 |

Number of pages | 21 |

Journal | Taiwanese Journal of Mathematics |

Volume | 10 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2006 Mar |

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### Keywords

- Asymptotic behavior
- Blow-up
- Fixed-point theory

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Taiwanese Journal of Mathematics*,

*10*(3), 807-827. https://doi.org/10.11650/twjm/1500403862