A subdifferential formulation of fourth order singular diffusion equations

Kashima, Y.

Hokkaido University Preprint Series in Mathematics, 2003, 598, [1]

Permalink : https://doi.org/10.14943/83743

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アクセス権	open access
DOI	https://doi.org/10.14943/83743
URI	https://hdl.handle.net/2115/69347
タイトル	A subdifferential formulation of fourth order singular diffusion equations
著者	著者名 Kashima, Y.
言語	英語
発行日	2003-08
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	598
ページ	[1]
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record