Some applications of (C ₀,1)-semigroups

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 (C ₀,1) -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.