  We consider the mathematical treatment of a system of nonlinear partial
differential equations based on a model, proposed in 1972 by J. Newman, in
which the coupling between the Lithium concentration, the phase potentials and
temperature in the electrodes and the electrolyte of a Lithium battery cell is
considered. After introducing some functional spaces well-adapted to our
framework we obtain some rigorous results showing the well-posedness of the
system, first for some short time and then, by considering some hypothesis on
the nonlinearities, globally in time. As far as we know, this is the first
result in the literature proving existence in time of the full Newman model,
which follows previous results by the third author in 2016 regarding a
simplified case.
