A time-dependent free boundary problem modeling the visual image in electrophotography (Q1309697)

The authors study a time-dependent free boundary problem arising in electrophotography: The formation of a visual image can be modeled through the electric potential \(-u\) satisfying \(\Delta u=1\) in the toner region and \(\Delta u=0\) outside this region. On the moving interface between the two regions an interface condition has to be added. It is shown that this problem has a smooth local solution which, for a special version of the interface condition, turns out to be unique.