## Analysis for a molten carbonate fuel cell

### Summary

Summary: In this paper we analyze a planar model for a molten carbonate electrode of a fuel cell. The model consists of two coupled second-order ordinary differential equations, one for the concentration of the reactant gas and one for the potential. Restricting ourselves to the case of a positive reaction order in the Butler-Volmer equation, we consider existence, uniqueness, various monotonicity properties, and an explicit approximate solution for the model. We also present an iteration scheme to obtain solutions, and we conclude with a few numerical examples.

### Mathematics Subject Classification

80A30, 34A45, 34A46

### Keywords/Phrases

electron.n.chemistry, fuel cells, butler-volmer equation, deadcore, existence, uniqueness and approximate solutions