This growth law arises in many physical situations, including aggregation of diffusing particles, electrodeposition, and viscous fingering at a fluid-fluid boundary. One can think of the evolution as the growth of needle crystals by deposition of material. The singular nature of the Green's function means that all growth is at the tip, so that slit domains stay slit domains. We were able to describe the evolution exactly of certain slit domains like the one shown. At any time, a needle tip may bifurcate into two tips growing at an angle to each other.
Every solution has infinitely many other solutions tangent to it at every point.
This research project was continued by the 1992 REU group .