Abstract
The formation of a visual image in electrophotography can be modeled as a time-dependent free boundary problem. The electric potential &-u satisfies Δu=1 in the toner region and Δu=0 outside this region, whereas on the interface (which is a moving boundary)-∂u/∂N=velocity of the interface, N being the outward normal to the toner region. It is proved that this problem has a smooth solution for a small time interval; furthermore, for a certain version of the free boundary condition, the solution is unique.
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References
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Communicated by R. V. Kohn
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Friedman, A., Velázquez, J.J.L. A time-dependent free boundary problem modeling the visual image in electrophotography. Arch. Rational Mech. Anal. 123, 259–303 (1993). https://doi.org/10.1007/BF00375128
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DOI: https://doi.org/10.1007/BF00375128