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**On the existence of a weak solution of a half-cell model for PEM fuel cells.**
*(English)*
Zbl 1197.34028

Summary: 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 T. Zhou and H. T. Liu [in: Proceeding of the ASME Heat Transfer Division, 43–49, Orlando, Fla, USA, 2000 (2000); Int. J. Transport Phenomena 3, No. 3, 177–198 (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 \(H^{1}\).

### MSC:

34B15 | Nonlinear boundary value problems for ordinary differential equations |

34B60 | Applications of boundary value problems involving ordinary differential equations |

47N20 | Applications of operator theory to differential and integral equations |

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\textit{S.-J. Chern} and \textit{P.-C. Huang}, Math. Probl. Eng. 2010, Article ID 701096, 16 p. (2010; Zbl 1197.34028)

### References:

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