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MACHIHARA Shuji

Faculty: Graduate School of Science and Engineering TEL:
Position: Professor ■FAX:
Address: 255 Shimo-Okubo, Sakura-ku, Saitama City, Saitama 338-8570, JAPAN ■Mail Address:
■Web site:

Profile

Assigned Class

Faculty of Science

Research Field

Basic analysis
keyword:Nonlinear partial differential equation

Current Subject

keyword:Nonlinear wave equations , Existence of solutions

Academic Background

Graduate School
Hokkaido University , () , 2002(Completed)
University of Tokyo , () , 1998(Completed)
College
Waseda University , 1996(Graduated)
Degree

Research Career

Research Career
2007 - 現在 ,
2006 - 2007 ,
2002 - 2006 ,

Research

Books, Articles, etc.

Articles
Generalizations of the logarithmic Hardy inequality in critical Sobolev-Lorentz spaces
,Journal of Inequalities and Applications 2013
Shuji Machihara, Tohru Ozawa and Hidemitsu Wadade

Some inequalities related to the Lorentz spaces
,Hokkaido Mathematical Journal,42:247--267 2013
Shuji Machihara and Tohru Ozawa

Hardy type inequalities on balls
,Tohoku Mathematical Journal,65:321--330 2013
Shuji Machihara, Tohru Ozawa and Hidemitsu Wadade

Local and global well posedness for the Chern-Simons-Dirac system in one dimension
,Differential and Integral Equations. An International Journal for Theory & Applications,25:699--718 2012
Bournaveas, Nikolaos and Candy, Timothy and Machihara, Shuji

Well-posedness for nonlinear Dirac equations in one dimension
,Kyoto J. Math.,2:403-451 2010
Machihara, Shuji and Nakanishi, Kenji and Tsugawa, Kotaro

Scattering Theory for the Dirac Equation with a Nonlocal Term
,Proceedings of the Royal Society of Edinburgh, Section 139A:867–878 2009
Shuji Machihara and Kimitoshi Tsutaya

Dirac equation with certain quadratic nonlinearities in one space dimension
,Communications in Contemporary Mathematics,9:421-435 2007
Shuji Machihara

The Cauchy problem for the 1-D Dirac--Klein--Gordon equation
,Nonlinear Differential Equations and Applications NoDEA,14:625-641 2007
Shuji Machihara

The explicit solutions to the nonlinear Dirac equation and Dirac-Klein-Gordon equation
,Ricerche di Matematica,56:19-30 2007
Shuji Machihara and Takayuki Omoso

Bilinear estimates for the transport equations
,Advanced Studies in Pure Mathematics-Asymptotic Analysis and Singularities,47(1):189-196 2007
Shuji Machihara

Endpoint Strichartz estimates and global solutions for the nonlinear Dirac equation
,Journal of Functional Analysis,219:1-20 2005
Shuji Machihara, Makoto Nakamura, Kenji Nakanishi and Tohru Ozawa

One dimensional Dirac equation with quadratic nonlinearities
,Discrete and Continuous Dynamical Systems - Series A,13:277-290 2005
Shuji Machihara

Small global solutions for nonlinear Dirac equations
,Differential Integral Equations,17:623-636 2004
Shuji Machihara, Makoto Nakamura and Tohru Ozawa

Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation
,Revista Matem'atica Iberoamericana,19:179-194 2003
Shuji Machihara, Kenji Nakanishi and Tohru Ozawa

Interpolation inequalities in Besov spaces
,Proceedings of the American Mathematical Society,131(5):1553-1556 2003
Shuji Machihara and Tohru Ozawa

The inviscid limit for the complex Ginzburg—Landau equation
,Journal of Mathematical Analysis and Applications,281:552-564 2003
Shuji Machihara and Yoshihisa Nakamura

Nonrelativistic limit in the energy space for nonlinear Klein--Gordon equations
,Mathematische Annalen,322:603-621 2002
Shuji Machihara, Kenji Nakanishi and Tohru Ozawa

Small data global solutions for Dirac--Klein--Gordon equation
,Differential and Integral Equations,15:1511-1517 2002
Shuji Machihara

The Nonrelativistic Limit of the Nonlinear Klein--Gordon Equation
,Funkcialaj Ekvacioj,44:243-252 2001
Shuji Machihara

Presentation
空間 1 次元 2 次の非線形項をもつ Dirac 方程式系の初期値問題について
日本数学会 2013 年度秋季総合分科会,函数方程式分科会アブストラクト 201309
町原秀二

Maximal operators associated to the wave equation
エジンバラ大学解析セミナー 201101
Shuji Machihara

Hardy inequalities and maximal operators associated to the wave equation
バーミンガム大学数学講演会 201011
Shuji Machihara