2022-05-24T16:26:51Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/692802018-04-25T23:44:08Zhdl_2115_45007hdl_2115_116Quasi-static evolution of 3-D crystals grown from supersaturated vaporGiga, Y.Rybka, P.410Gonda and Gorni (T.Gonda, H.Gomi, Ann. Glaciology, 6 (1985), 222 224) have grown large elongated ice crystals from supersaturated vapor. Theoretrically this problem may be recast in a framework similar to that used by Seeger (A.Seeger, Philos. Mag., ser. 7, 44, no 348, (1953) 1-13) for studies of planar crystals. The resulting set of equations is of Stefan type. We also include the GibbsÂThomson relation on the crystal surface. In order to make this system tractable mathematically we assume that the \\\1lff crystal is a fixed cylinder. Subsequently we study a weak form of our system. We show local in time existence of solutions assuming that the initial shape is an arbitrary cylinder. We comment on properties of weak solutions.Departmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69280info:doi/10.14943/83676https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69280/1/pre530.pdfHokkaido University Preprint Series in Mathematics5301162001-06engpublisher