  A mathematical model of nonlinear radiation is introduced into a
thermoelectrochemical problem, and its qualitative analysis is focused on
existence of solutions. The main objective is the nonconstant character of each
parameter, that is, the coefficients are assumed to be depend on the spatial
variable and the temperature. Making recourse of known estimates of solutions
for some auxiliary elliptic and parabolic problems, which are explicitly
determined by the Gehring-Giaquinta-Modica theory, we find sufficient smallness
conditions on the data to the existence of the original solutions via the
Schauder fixed point argument. These conditions may provide useful informations
for numerical as well as real applications. We conclude with an example of
application, namely the electrolysis of molten sodium chloride.
