Interface dynamics equations: their properties and computer simulation
  We investigate the interface dynamic in Laplacian growth model, using the conformal mapping technique. Starting from the governing equation for the conformal map, obtained by B.Shraiman and D.Bensimon, we derive different possible forms of the equation. Some of them have evident physical representation and are convenient for computer simulation, the results of which are presented in this paper. 
V.Gafiychuk, A.Shnyr, B.Datsko (Institute of Applied Problems of   Mechanics and Mathematics, National Academy of Science of...