  The Cahn-Hilliard reaction model, a nonlinear, evolutionary PDE, was
introduced to model phase separation in lithium-ion batteries. Using
Butler-Volmer kinetics for electrochemical consistency, this model allows
lithium-ions to enter the domain via a nonlinear Robin-type boundary condition
$\partial_\nu \mu = R(c,\mu)$ for the chemical potential $\mu$, with $c$, the
lithium-ion density. Importantly, $R$ depends exponentially on $\mu$. Fixed
point methods are applied to obtain existence of regular solutions of the
Cahn-Hilliard reaction model in dimension $3,$ allowing for recovery of
exponential boundary conditions as in the physical application.
