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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
2018 ,
2014 - 2018 ,
2007 - 2014 ,
2006 - 2007 ,
2002 - 2006 ,

Research

Books, Articles, etc.

Articles
Non-delay limit in the energy space from the nonlinear damped wave equation to the nonlinear heat equation
,Journal of Hyperbolic Differential Equations,19(3):407--437 2022
Takahisa Inui and Shuji Machihara

Spherical harmonics and Hardy's inequalities
,数理解析研究所講究録,2235:92-102 2022
Shuji Machihara

Sharp ill-posedness of the Dirac-Klein-Gordon system in one dimension
,Nonlinear Anal.,192:111687, 11 2020
Machihara, Shuji and Okamoto, Mamoru

A supersolutions perspective on hypercontractivity
,Ann. Mat. Pura Appl. (4),199:2105--2116 2020
Aoki, Yosuke and Bennett, Jonathan and Bez, Neal and Machihara, Shuji and Matsuura, Kosuke and Shiraki, Shobu

Blowup solutions for the nonlinear {S}chr\"{o}dinger equation with complex coefficient
,Differential Integral Equations,33:445--464 2020
Kawakami, Shota and Machihara, Shuji

Global wellposedness for a one-dimensional Chern-Simons-Dirac system in L^p
,Comm. Partial Differential Equations,42:1175-1198 2017
Shuji Machihara, Takayoshi Ogawa

Remarks on the Rellich inequality
,Math. Z.,286:1367–1373 2017
Shuji Machihara, Tohru Ozawa and Hidemitsu Wadade

Well-posedness and ill-posedness of the Cauchy problem for the generalized Thirring model
,Differential Integral Equations,29:401--420 2016
Hyungjin Huh, Shuji Machihara and Mamoru Okamoto

Remarks on the ill-posedness for the Dirac-Klein-Gordon system
,Dyn. Partial Differ. Equ.,13:179--190 2016
Shuji Machihara and Mamoru Okamoto

Extremisers for the trace theorem on the sphere
,Mathematical Research Letters,23:633--647 2016
Bez Neal, Shuji Machihara and Mitsuru Sugimoto

Sharp well-posedness and ill-posedness for the Chern-Simons-Dirac system in one dimension
,Int. Math. Res. Not. IMRN,6:1640--1694 2016
Shuji Machihara and Mamoru Okamoto

Remark on a semirelativistic equation in the energy space
,Discrete Contin. Dyn. Syst., Dynamical systems, differential equations and applications. 10th AIMS Conference. Suppl.:473--478 2015
Ozawa, Tohru and Machihara, Shuji and Fujiwara, Kazumasa

Scaling invariant Hardy inequalities of multiple logarithmic type on the whole space
,J. Inequal. Appl. 2015
Machihara, Shuji and Ozawa, Tohru and Wadade, Hidemitsu

On a system of semirelativistic equations in the energy space
,Commun. Pure Appl. Anal.,14:1343—1355 2015
Fujiwara, Kazumasa and Machihara, Shuji and Ozawa, Tohru

Well-posedness for the Cauchy problem for a system of semirelativistic equations
,Comm. Math. Phys.,338:367—391 2015
Fujiwara, Kazumasa and Machihara, Shuji and Ozawa, Tohru

Ill-posedness of the Cauchy problem for the Chern-Simons-Dirac system in one dimension
,J. Differential Equations,258:1356—1394 2015
Machihara, Shuji and Okamoto, Mamoru

Notes on the paper entitled `Generalizations of the logarithmic Hardy inequality in critical Sobolev-Lorentz spaces'
,Journal of Inequalities and Applications,253:2 2014
Machihara, Shuji and Ozawa, Tohru and Wadade, Hidemitsu

On the semilinear Schr\"odinger equation with time dependent coefficients
,Mathematische Nachrichten,287:1986--2001 2014
Gonda, Takuya and Machihara, Shuji and Ozawa, Tohru

A note on the Chern-Simons-Dirac equations in the Coulomb gauge
,Discrete and Continuous Dynamical Systems. Series A,34:2693--2701 2014
Bournaveas, Nikolaos and Candy, Timothy and Machihara, Shuji

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Dirac-Klein-Gordon方程式初期値問題の非適切性の議論
第10回実解析と函数解析による偏微分方程式論研究集会 281226
町原秀二

Ill-posedness results for the 1d Dirac-Klein-Gordon sytem
Interactions Between Harmonic and Geometric Analysis 281129
Shuji Machihara

L2直交性から眺める Rellich の不等式
「解析学とその周辺」＠野田 202210
町原　秀二

等式から眺める Rellich の不等式
九州関数方程式セミナー 202205
町原　秀二

Spherical harmonics and Hardy's inequalities
RIMS共同研究(公開型)「量子場の数理とその周辺」:10 202112
町原　秀二

球面微分とハーディの不等式
Workshop on Analysis in Kagurazaka 2021 202101
町原秀二

Spherical Harmonics and Hardy’s equality
Recent Progress on Dispersive and Wave Equations 202002
町原秀二

The range of Sobolev regularity for the well-posedness of the Dirac-Klein-Gordon system in 1d
第11回名古屋微分方程式研究集会 201903
町原秀二

非線形シュレディンガー方程式の有限時間爆発解に対する注意
反応拡散方程式と非線形分散型方程式の解の挙動 201902
町原秀二

The range of Sobolev regularity for the well-posedness of the Dirac-Klein-Gordon system in 1d
Workshop on nonlinear wave equations and related topics in Kobe 201811
町原秀二

空間１次元Dirac-Klein-Gordon方程式の初期値問題の適切性について
日本数学会実函数論分科会, 函数解析学分科会共催 第56回実函数論・函数解析学合同シンポジウム,第56回実函数論・函数解析学 合同シンポジウム 講演集:137 - 147 201708
町原秀二

Global well-posedness for one dimensional Chern-Simons-Dirac system in Lp
Nonlinear Partial Differential Equations for Future Applications: Hyperbolic and Dispersive PDE 201707
Shuji Machihara

Remarks on the ill-posedness for the Dirac-Klein-Gordon system
International Workshop on ``Fundamental Problems in Mathematical and Theoretical Physics” 201707
Shuji Machihara

The Cauchy problem for the Chern-Simons-Dirac equation in one spatial dimension
名古屋微分方程式セミナー（名古屋大学） 201601
町原秀二

Ill-posedness for the Cauchy problem of the Dirac-Klein-Gordon system in one dimension
Critical problems in nonlinear evolution equations（東京理科大学） 201511
町原秀二

空間1次元Chern-Simons-Dirac方程式系の初期値問題の非適切性
調和解析駒場セミナー 201511

空間1次元Dirac-Klein-Gordon方程式系の初期値問題
南大阪応用数学セミナー（大阪市立大） 201511
町原秀二

Ill-posed results for the 1d Dirac-Klein-Gordon system
10th International ISAAC Congress 201508
町原秀二

Well-posed and Ill-posed results for the 1d Dirac-Klein-Gordon system
Harmonic Analysis and Partial Differential Equations(ICMS) 201507
町原秀二

空間1次元Chern-Simons-Dirac方程式の初期値問題の適切性と非適切性
第122回神楽坂解析セミナー（東京理科大学） 201404
町原秀二

Generalized Thirring model in one dimension
韓国中央大学校セミナー 201403
町原秀二

Hardyの不等式について
第７回 実解析と函数解析による微分方程式セミナー 201312
町原秀二

空間 1 次元 Chern-Simons-Dirac 方程式の適切性について
神戸解析セミナー 201312
町原秀二

Local and global well-posedness of the Cauchy problem for the Chern-Simons-Dirac system in one dimension
韓国中央大学校セミナー 201311
町原秀二

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

空間1次元Chern-Simons-Dirac方程式の初期値問題の適切性について
なかもず解析セミナー 201306
町原秀二

空間一次元 Chern-Simons-Dirac 方程式の非適切性
前橋セミナー 201305
町原秀二

空間1次元Chern-Simons-Dirac方程式の1点集約制御と時間大域可解性
北海道大学波動セミナー 201301
町原秀二

Global wellposedness for one dimensional Chern-Simons-Dirac system in L^p
名古屋大学微分方程式セミナー 201211
町原秀二

1+1次元 Chern-Simons-Dirac方程式のL^p時間大域適切性
2012年度日本数学会,日本数学会2012年度秋季総合分科会函数方程式論分科会講演アブストラクト:170--171 201209
町原秀二

1+1次元Chern-Simons-Dirac方程式の1点集約制御と時間大域解
第11回葉山セミナー 201209
町原秀二

Chern-Simons-Dirac 方程式の臨界Lp 空間における時間大域可解性
発展方程式シンポジウム 201203
町原秀二

波動方程式解最大関数の有界性
第5回実解析と函数解析による微分方程式セミナー 201112
町原秀二

空間1 次元Chern-Simons-Dirac 方程式の時間大域解
弘前非線形方程式研究会 201112
町原秀二

Time local and global well-posedness for the Chern-Simons-Dirac System in one dimension
京都NLPDEセミナー 201107
町原秀二

Time local and global existence for Chern-Simons-Dirac equation in onespace dimension
東北大学応用数学セミナー 201107
町原秀二

Local and Global well-posedness for the Chern-Simons-Dirac System in One Dimension
九州関数方程式セミナー 201106
町原秀二

Boundedness for the maximal function associated with the wave equation
応用解析学研究会 201105
町原秀二

Local and global existence for Chern-Simons-Dirac equation in one space dimension
さいたま数理解析セミナー 201104
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