Very Singular Diffusion Equations-Second and Fourth Order Problems

Giga, Mi-Ho; Giga, Yoshikazu

Hokkaido University Preprint Series in Mathematics, 2010, 960, 1-33

Permalink : https://doi.org/10.14943/84107

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アクセス権	open access
DOI	https://doi.org/10.14943/84107
URI	https://hdl.handle.net/2115/69767
タイトル	Very Singular Diffusion Equations-Second and Fourth Order Problems
著者	著者名 Giga, Mi-Ho
著者	著者名 Giga, Yoshikazu
言語	英語
キーワード	total variation flow
	singular diffusion
	fourth order model
	jump discontinuity
	image analysis
	crystalline flow
発行日	2010-05-06
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	960
ページ	1-33
抄録	This paper studies singular diffusion equations whose diffusion effect is so strong that the speed of evolution becomes a nonlocal quantity. Typical examples include the total variation flow as well as crystalline flow which are formally of second order. This paper includes fourth order models which are less studied compared with second order models. A typical example of this model is an H−1 gradient flow of total variation. It turns out that such a flow is quite different from the second order total variation flow. For example, we prove that the solution may instantaneously develop jump discontinuity for the fourth order total variation flow by giving an explicit example.
資源タイプ	紀要論文
出版タイプ	Version of Record