SAKAGUCHI Shigeru

J-GLOBAL         Last updated: Jun 12, 2018 at 12:30
 
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Name
SAKAGUCHI Shigeru
Affiliation
Tohoku University
Section
Graduate School of Information Sciences
Job title
Professor
Degree
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

 
 

Academic & Professional Experience

 
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 simple proof of a strong comparison principle for semicontinuous viscosity solutions of the prescribed mean curvature equation
Masaki Ohnuma and Shigeru Sakaguchi
arXiv:1806.03587v1    Jun 2018
Two-phase heat conductors with a surface of the constant flow property
Lorenzo Cavallina, Rolando Magnanini, and Shigeru Sakaguchi
arXiv:1801.01352v1    Jan 2018
Two-phase heat conductors with a stationary isothermic surface and their related elliptic overdetermined problems
Shigeru Sakaguchi
RIMS Kôkyûroku Bessatsu   accepted for publication    Mar 2018   [Refereed][Invited]
An over-determined boundary value problem arising from neutrally coated inclusions in three dimensions
Hyeonbae Kang, Hyundae Lee, and Shigeru Sakaguchi
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze   16(4) 1193-1208   Dec 2016   [Refereed]
Two-phase heat conductors with a stationary isothermic surface
Shigeru Sakaguchi
Rendiconti dell'Istituto di Matematica dell'Universita di Trieste   48 167-187   Dec 2016   [Refereed][Invited]

Books etc

 
Geometry of solutions of partial differential equations
SAKAGUCHI Shigeru
Saiensu-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