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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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References:

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