## Journal of Applied Mathematics

### Some Applications of $({C}_{0},1)$-Semigroups

#### 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 $({C}_{0},1)$-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.

#### Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 968760, 14 pages.

Dates
First available in Project Euclid: 14 December 2012

https://projecteuclid.org/euclid.jam/1355495122

Digital Object Identifier
doi:10.1155/2012/968760

Mathematical Reviews number (MathSciNet)
MR2915732

Zentralblatt MATH identifier
1245.49006

#### Citation

Chang, Yu-Hsien; Hong, Cheng-hong. Some Applications of $({C}_{0},1)$ -Semigroups. J. Appl. Math. 2012 (2012), Article ID 968760, 14 pages. doi:10.1155/2012/968760. https://projecteuclid.org/euclid.jam/1355495122