日本語English

# SAKAGUCHI Shigeru

Last updated: Jan 20, 2020 at 12:42

Name SAKAGUCHI Shigeru Tohoku University Graduate School of Information Sciences Professor Doctor of Science(Tokyo Metropolitan University)

## Profile

The main purpose is to know geometric properties of solutions of partial differential equations. Since solutions are functions, it is natural to want to know their shapes and geometric properties. The current research topics are the following.

(1) Stationary level surfaces of solutions of diffusion equations: To know the shapes of graphs of functions, one may begin by investigating their level surfaces. In particular, an isothermic surface of the solution of the heat equation is called stationary if its temperature depends only on time. The existence of a stationary isothermic surface is deeply related to the symmetry of the heat conductor. The right helicoid, the circular cylinder, the sphere and the plane are examples of stationary isothermic surfaces in Euclidean 3-space. The characterization of the circular cylinder, the sphere and the plane by using stationary isothermic surfaces in Euclidean 3-space is almost completed, and similar good characterization of the right helicoid is wanted.

(2) Problems of partial differential equations on composite materials: Very recently, we considered the heat diffusion over composite media and we got a characterization of the spherical shell by using either stationary isothermic surfaces or surfaces with the constant flow property among two-phase heat conductors. In particular, we are interested in problems dealing with composite materials.

(3) Interaction between diffusion and geometry of domain: The shape of the heat conductor is deeply related to the initial heat diffusion. Diffusion equations we consider are the heat equation, the porous medium type equation, and their related equations.

(4) Shapes of solutions of elliptic equations: In general, solutions of elliptic equations describe steady states after a sufficiently long time. Liouville-type theorems characterize hyperplanes as graphs of entire solutions with some restriction. Overdetermined boundary value problems characterize some symmetrical domains. Isoperimetric inequalities accompanied by boundary value problems characterize shapes of the solutions which give the equalities.

(5) The point of view of inverse problems: Partial differential equations appear in models describing natural phenomena. There are many interesting problems which characterize some geometry in some reasonable way from the point of view of inverse problems.

## Research Areas

Apr 2012
-
Today
Professor, Tohoku University

Apr 2008
-
Mar 2012
Professor, Hiroshima University

Feb 2002
-
Mar 2008
Professor, Ehime University

Apr 1993
-
Jan 2002
Associate Professor, Ehime University

Apr 1989
-
Mar 1993
Research Associate, Tokyo Institute of Technology

## Education

-
1986
Mathematics, Graduate School, Division of Natural Science, Tokyo Metropolitan University

-
1979
Faculty of Science, Tokyo Institute of Technology

## Committee Memberships

2003
-
2007
Mathematical Society of Japan

2007
-
2007
Mathematical Society of Japan

## Awards & Honors

Sep 2012
Geometry on the domain via the isothermic set for diffusion equations, 2012 Analysis Prize, The Mathematical Society of Japan

## Published Papers

A construction of patterns with many critical points on topological tori
Putri Zahra Kamalia and Shigeru Sakaguchi
arXiv:1912.01872v1    Dec 2019
Neutral inclusions, weakly neutral inclusions, and an over-determined problem for confocal ellipsoids
Yong-Gwan Ji, Hyeonbae Kang, Xiaofei Li and Shigeru Sakaguchi
arXiv:2001.04610v1    Jan 2020
Polarization tensor vanishing structure of general shape: Existence for small perturbations of balls
Hyeonbae Kang, Xiaofei Li and Shigeru Sakaguchi
arXiv:1911.07250v2    Jan 2020
A characterization of a hyperplane in two-phase heat conductors
Lorenzo Cavallina, Shigeru Sakaguchi and Seiichi Udagawa
arXiv:1910.06757v1    Oct 2019
Some characterizations of parallel hyperplanes in multi-layered heat conductors
Shigeru Sakaguchi
arXiv:1905.12380v1    May 2019

## Books etc

 Geometry of solutions of partial differential equationsSAKAGUCHI ShigeruSaiensu-sha Co., Ltd. Publishers   Mar 2017

## Research Grants & Projects

Geometry of partial differential equations and inverse problems
Japan Society for the Promotion of Science: Grant-in-Aid for Scientific Research (B)
Project Year: Apr 2018 - Mar 2022    Investigator(s): SAKAGUCHI Shigeru
Transmission problems in composite media and overdetermined problems with transmission conditions
Japan Society for the Promotion of Science: Grant-in-Aid for Challenging Exploratory Research
Project Year: Apr 2016 - Mar 2019    Investigator(s): SAKAGUCHI Shigeru
Geometry of solutions of partial differential equations and the inverse problems accompanied by it
Japan Society for the Promotion of Science: Grant-in-Aid for Scientific Research (B)
Project Year: Apr 2014 - Mar 2018    Investigator(s): SAKAGUCHI Shigeru
Search for new isoperimetric inequalities relating to elliptic equations
Japan Society for the Promotion of Science: Grant-in-Aid for challenging Exploratory Research
Project Year: Apr 2013 - Mar 2016    Investigator(s): SAKAGUCHI Shigeru
Diffusion and geometry of domain
Japan Society for the Promotion of Science: Grant-in-Aid for Scientific Research (B)
Project Year: Apr 2008 - Mar 2013    Investigator(s): SAKAGUCHI Shigeru