  In the paper a mathematical model of the PEN structure (positive electrode -
electrolyte - negative electrode) of the Solid Oxide Fuel Cell (SOFC) is
analyzed. It is proved that classical formulation of the problem leads
inevitably to locally unphysical effects related to negative values of the
activation overpotential. Moreover, the active layers' thicknesses are shown to
be components of solution and cannot be predefined in an arbitrary way. A
modified mathematical formulation of the problem is proposed which includes
this novelty alongside an amended definition of the activation overpotential. A
dedicated computational scheme is developed for the cathode sub-problem. The
accuracy of computations is investigated by means of a newly introduced
analytical benchmark example. The numerical results obtained for LSCF cathode
are used to discuss certain aspects of the modified formulation and the active
layer thickness. The new modelling approach is validated by comparison with
experimental data.
