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Hokkaido University Preprint Series in Mathematics >
Stability of facets of self-similar motion of a crystal
| Title: | Stability of facets of self-similar motion of a crystal |
| Authors: | Giga, Yoshikazu Browse this author | | Rybka, Piotr Browse this author |
| Issue Date: | 12-Mar-2004 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 636 |
| Start Page: | 1 |
| End Page: | 28 |
| Abstract: | We are concerned with a quasi-steady Stefan type problem with Gibbs-Thomson relation and the mobility term which is a model for a crystal growing from supersaturated vapor. The evolving crystal and the Wulff shape of the interfacial energy are assumed to be (right-circular) cylinders. In pattern formation deciding what are the conditions which guarantee that the speed in the normal direction is constant over each facet, so that the facet does not break, is an important question. We formulate such a condition with an aid of a convex variational problem with a convex obstacle type constraint. We derive necessary and sufficient conditions for the non-breaking of facets in terms of the size and the supersaturation at space infinity when the motion is self-similar. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69443 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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