Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >
Very Singular Diffusion Equations-Second and Fourth Order Problems
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 |
Publisher: | Department of Mathematics, Hokkaido University |
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
|