|
Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >
Periodic total variation flow of non-divergence type in R^n
| Title: | Periodic total variation flow of non-divergence type in R^n |
| Authors: | Giga, Mi-Ho Browse this author | | Giga, Yoshikazu Browse this author | | Pozar, Norbert Browse this author |
| Keywords: | phase transitions | | curvature flows | | crystalline mean curvature | | total variation flow | | viscosity solutions | | comparison theorems |
| Issue Date: | 6-Feb-2013 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1029 |
| Start Page: | 1 |
| End Page: | 36 |
| Abstract: | We introduce a new notion of viscosity solutions for a class of very singular nonlinear parabolic problems of non-divergence form in a periodic domain of arbitrary dimension, whose di usion on flat parts with zero slope is so strong that it becomes a nonlocal quantity. The problems include the classical total variation flow and a motion of a surface by a crystalline mean curvature. We establish a comparison principle, the stability under approximation by regularized parabolic problems, and an existence theorem for general continuous initial data. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/70238 |
| 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
|
