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A subdifferential formulation of fourth order singular diffusion equations
| Title: | A subdifferential formulation of fourth order singular diffusion equations |
| Authors: | Kashima, Y. Browse this author |
| Issue Date: | Aug-2003 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 598 |
| Start Page: | [1] |
| Abstract: | A fourth order equation with singular diffusivity, which is a model of relaxation dynamics for crystalline surfaces driven by surface diffusion, is formulated. The notion of subdifferentials enables us to formulate the singular diffusion equation mathematically as a gradient flow equation in the Sobolev space of negative power H-1. The subdifferential of the singular energy in H-1 is calculated. Moreover, the speed of a special profile is calculated for one dimensional problem. It turns out that a seemingly natural free boundary formulation with facets is inconsistent with a subdifferential formulation which can be approximated by a smooth energy. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69347 |
| 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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