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

Giga, Mi-Ho; GIGA, Yoshikazu; Ohtsuka, Takeshi et al.

Hokkaido University Preprint Series in Mathematics, 2012, 998, 1-23

Permalink : https://doi.org/10.14943/84145

このアイテムのアクセス数:1,067件（2026-10-18 07:43 集計）

ファイル	フォーマット	サイズ	閲覧回数	説明
re998	pdf	191 KB	680

アクセス権	open access
DOI	https://doi.org/10.14943/84145
URI	https://hdl.handle.net/2115/69804
タイトル	On behavior of signs for the heat equation and a diffusion method for data separation
著者	Giga, Mi-Ho ; GIGA, Yoshikazu ; Ohtsuka, Takeshi ; Umeda, Noriaki
著者名 Giga, Mi-Ho
著者名 GIGA, Yoshikazu
著者名 Ohtsuka, Takeshi
著者名 Umeda, Noriaki
言語	英語
発行日	2012-02-13
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	998
ページ	1-23
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record