Copyright © 2012 Yu-Hsien Chang and Cheng-hong Hong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This study is originally motivated by the thermal balance equations for the gas and solid interphase heat-transfer for the fast-igniting catalytic converter of automobiles. Instead of solving this problem directly, we proved some results concerning the existence and uniqueness for abstract semilinear initial value problem by means of -semigroup theories on locally convex topological space. The most enjoyable here is that these results not only can be applied to solve the interphase heat-transfer for the fast-igniting catalytic converter of automobile under the situation of preheating at the entry edge of converter, but also can be applied to some other practical problems.