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Periodic total variation flow of non-divergence type in R^n

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84424

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
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

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