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) = 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.
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 |
Externally published | Yes |
Keywords
- Asymptotic behavior
- Blow-up
- Fixed-point theory
ASJC Scopus subject areas
- Mathematics(all)