THE BEHAVIOR OF THE INTERPHASE HEAT-TRANSFER FOR THE FAST-IGNITING CATALYTIC CONVERTER

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: $$ \left\{ \begin{array}{ll} \frac{\partial}{\partial t} u(t,x) = -\alpha \frac{\partial}{\partial x} u(t,x) + av(t,x) - au(t,x) & \text{ for } t \gt 0, 0 \lt x \lt l; \\ \frac{\partial}{\partial t} v(t,x) = bu(t,x) - bv(t,x) + \lambda \exp(v(t,x)) & \text{ for } t \gt 0, 0 \lt x \lt l; \\ u(t,0) = \eta & \text{ for } t \geq 0; \\ u(0,x) = u_{0}(x) \text{ and } v(0,x) = v_{0}(x) & \text{ for } x \gt 0. \end{array} \right. $$ where $u_{0}$, $v_{0}$ are continuous functions on $[0,l]$ with $u_{0}(0) = \eta$. 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.