## 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
Full Text:

### References:

 [1] K. Promislow and B. Wetton, “PEM fuel cells: a mathematical overview,” SIAM Journal on Applied Mathematics, vol. 70, no. 2, pp. 369-409, 2009. · Zbl 1189.35002 [2] T. Zhou and H. Liu, “3-D model of proton exchange membrane fuel cells,” in Proceeding of the ASME Heat Transfer Division, pp. 43-49, Orlando, Fla, USA, 2000. [3] V. Gurau and J. A. Adin Mann Jr., “A critical overview of computational fluid dynamics multiphase models for proton exchange membrane fuel cells,” SIAM Journal on Applied Mathematics, vol. 70, no. 2, pp. 410-454, 2009. · Zbl 1404.92228 [4] V. Gurau, F. Barbir, and H. Liu, “An analytic solution of a half-cell model for PEM fuel cells,” Journal of the Electrochemical Society, vol. 147, pp. 2468-2477, 2000. [5] V. Gurau, H. Liu, and S. Kaka\cc, “Two-dimensional model for proton exchange membrane fuel cells,” AIChE Journal, vol. 44, no. 11, pp. 2410-2422, 1998. [6] S. J. Chern, P. C. Huang, and C. A. Lin, “On the existence of a classical solution of a halfcell model for PEM fuel cells,” preprint, http://www.math.nthu.edu.tw/ sjchern/mdl-1-2010-march.pdf. · Zbl 1197.34028 [7] T. Zhou and H. T. Liu, “A general three-dimensional model for proton exchange membrane fuel cells,” International Journal of Transport Phenomena, vol. 3, pp. 177-198, 2001. [8] H. Liu, T. Zhou, and P. Cheng, “Transport phenomena analysis in proton exchange membrane fuel cells,” Journal of Heat Transfer, vol. 127, no. 12, pp. 1363-1379, 2005. [9] E. Zeidler, Nonlinear Functional Analysis and Its Applications. II, Springer, New York, NY, USA, 1990, translated by E. Zeidler and Leo F. Boron. · Zbl 0684.47029 [10] L. C. Evans, Partial Differential Equations, vol. 19 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, USA, 1998. · Zbl 0902.35002 [11] R. A. Adams, Sobolev Spaces, Pure and Applied Mathematics, vol. 6, Academic Press, New York, NY, USA, 1975. · Zbl 0527.55016 [12] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, vol. 224 of Grundlehren der Mathematischen Wissenschaften, Springer, Berlin, Germany, 2nd edition, 1983. · Zbl 0562.35001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.