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Hokkaido University Preprint Series in Mathematics >
Equations with singular diffusivity
| Title: | Equations with singular diffusivity |
| Authors: | Kobayashi, R. Browse this author | | Giga, Y. Browse this author |
| Keywords: | singular diffusivity | | faceted growth | | grain boundary | | extended gradient system |
| Issue Date: | 1-Aug-1998 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 420 |
| Start Page: | 1 |
| End Page: | 45 |
| Abstract: | Recently the models of the faceted crystal growth and of the grain boundary were proposed based on the gradient system with nondifferentiable energy. In this article, we study their most basic forms given by the equations ut = (ux/|ux|)x and ut = a/1(a * ux / ux)x where both of the related energy include luxl term of power one which is nondiffer entiable at Ux = 0. The first equation is spatially homogeneous while the second one is spatially inhomogeneous when a depends on x. These equations naturally express non-local interactions through their singular diffusivities ( Ux = 0) which make the profiles of the solutions completely flat. Mathematical basis for justifying and analyzing these equations will be explained, and also it will be shown how the solutions of the equations evolve by theoretical and numerical approach. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69170 |
| 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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