A time-dependent family of harmonic problems with boundary condition \(h(\partial \phi /\partial \nu)=\phi\), where h is a function dependent on the history of \(\phi\), models an electropaint process. It is proven that the problem has a weak solution \(\{\) \(\phi\) (x,t),h(x,t)\(\}\) and \(\lim_{t\to \infty} \phi (x,t)\) exists and coincides with the solution of an appropriate Signorini problem.