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Very Singular Diffusion Equations-Second and Fourth Order Problems

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84107

Title: Very Singular Diffusion Equations-Second and Fourth Order Problems
Authors: Giga, Mi-Ho Browse this author
Giga, Yoshikazu Browse this author
Keywords: total variation flow
singular diffusion
fourth order model
jump discontinuity
image analysis
crystalline flow
Issue Date: 6-May-2010
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 960
Start Page: 1
End Page: 33
Abstract: 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.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69767
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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