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Mathematical Problems in Engineering
Volume 2010, Article ID 701096, 16 pages
Research Article

On the Existence of a Weak Solution of a Half-Cell Model for PEM Fuel Cells

1Department of Mathematics, National Tsing-Hua University, Hsin-Chu 30013, Taiwan
2Department of Applied Mathematics, National Chiao-Tung University, Hsin-Chu 30010, Taiwan

Received 16 December 2009; Accepted 4 May 2010

Academic Editor: Katica R. (Stevanovic) Hedrih

Copyright © 2010 Shuh-Jye Chern and Po-Chun Huang. 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.


A nonlinear boundary value problem (BVP) from the modelling of the transport phenomena in the cathode catalyst layer of a one-dimensional half-cell single-phase model for proton exchange membrane (PEM) fuel cells, derived from the 3D model of Zhou and Liu (2000, 2001), is studied. It is a BVP for a system of three coupled ordinary differential equations of second order. Schauder's fixed point theorem is applied to show the existence of a solution in the Sobolev space 𝐻 1 .