TY - JOUR

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

AU - Chang, Yu Hsien

AU - Jau, Guo Chin

N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2006/3

Y1 - 2006/3

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

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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 -