THE BEHAVIOR OF THE INTERPHASE HEAT-TRANSFER FOR THE FAST-IGNITING CATALYTIC CONVERTER - Chang, Yu-Hsien; 張幼賢; Jau, Guo-Chin; 趙國欽 (Taiwanese journal of mathematics, 2006)
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: $\left\{ \begin{gathered} \frac{\partial }{{\partial t}}u(t,x) = - \alpha \frac{\partial }{{\partial x}}u(t,x) + a\upsilon (t,x) - au(t,x)fort > 0,0 < x < l; \hfill \\ \frac{\partial} {{\partial t}}\upsilon (t,x) = bu(t,x) - b\upsilon (t,x) + \lambda \exp\left( {\upsilon \left( {t,x} \right)} \right)fort > 0,0 < x < l; \hfill \\ u\left( {t,0} \right) = \eta fort \geqslant 0; \hfill \\ u(0,x) = {u_0}\left( x \right)and\upsilon \left( {0,x} \right) {\upsilon _0}(x)forx > 0 \hfill \\ \end{gathered} \right.$ where u₀, υ₀ 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.