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On behavior of signs for the heat equation and a diffusion method for data separation

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84145

Title: On behavior of signs for the heat equation and a diffusion method for data separation
Authors: Giga, Mi-Ho Browse this author
GIGA, Yoshikazu Browse this author
Ohtsuka, Takeshi Browse this author
Umeda, Noriaki Browse this author
Issue Date: 13-Feb-2012
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 998
Start Page: 1
End Page: 23
Abstract: Consider the solution u(x; t) of the heat equation with initial data u0. The diffusive sign SD[u0](x) is de ned by the limit of sign of u(x; t) as t ! 0. A sufficient condition for x 2 Rd and u0 such that SD[u0](x) is well-de ned is given. A few examples of u0 violating and ful lling this condition are given. It turns out that this diffusive sign is also related to variational problem whose energy is the Dirichlet energy with a delty term. If initial data is a difference of characteristic function of two disjoint sets, it turns out that the boundary of the set SD[u0](x) = 1 (or 􀀀1) is roughly an equi-distance hypersurface from A and B and this gives a separation of two data sets.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69804
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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