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

Pages (from-to) | 807-827 |

Number of pages | 21 |

Journal | Taiwanese Journal of Mathematics |

Volume | 10 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2006 Jan 1 |

### Fingerprint

### 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

**The behavior of the interphase heat-transfer for the fast-igniting catalytic converter.** / Chang, Yu Hsien; Jau, Guo Chin.

Research output: Contribution to journal › Article

*Taiwanese Journal of Mathematics*, vol. 10, no. 3, pp. 807-827. https://doi.org/10.11650/twjm/1500403862

}

TY - JOUR

T1 - The behavior of the interphase heat-transfer for the fast-igniting catalytic converter

AU - Chang, Yu Hsien

AU - Jau, Guo Chin

PY - 2006/1/1

Y1 - 2006/1/1

N2 - 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) = u0 (x) and v (0, x) = v0 (x) for x > 0. where u0, v0 are continuous functions on [0, l] with u0 (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.

AB - 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) = u0 (x) and v (0, x) = v0 (x) for x > 0. where u0, v0 are continuous functions on [0, l] with u0 (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.

KW - Asymptotic behavior

KW - Blow-up

KW - Fixed-point theory

UR - http://www.scopus.com/inward/record.url?scp=33750065709&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750065709&partnerID=8YFLogxK

U2 - 10.11650/twjm/1500403862

DO - 10.11650/twjm/1500403862

M3 - Article

AN - SCOPUS:33750065709

VL - 10

SP - 807

EP - 827

JO - Taiwanese Journal of Mathematics

JF - Taiwanese Journal of Mathematics

SN - 1027-5487

IS - 3

ER -