Analysis of properties of solutions to dispersive equations via canonical transforms and comparison principle

• Project/Area Number: 20340029
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Nagoya University
• Principal Investigator: SUGIMOTO Mitsuru 名古屋大学, 多元数理科学研究科, 教授 (60196756)
• Co-Investigator(Kenkyū-buntansha): TSUGAWA Kotaro 名古屋大学, 大学院・多元数理科学研究科, 准教授 (70402451) ; KATO Jun 名古屋大学, 大学院・多元数理科学研究科, 准教授 (00432237) ; HISHIDA Toshiaki 名古屋大学, 大学院・多元数理科学研究科, 教授 (60257243) ; MIYAKE Masatake 名古屋大学, 大学院・多元数理科学研究科, 教授 (70019496)
• Co-Investigator(Renkei-kenkyūsha): TACHIZAWA Kazuya 北海道大学, 大学院・理学研究院, 准教授 (80227090) ; TOMITA Naohito 大阪大学, 大学院・理学研究院, 准教授 (10437337)
• Project Period (FY): 2008 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥18,590,000 (Direct Cost: ¥14,300,000、Indirect Cost: ¥4,290,000); Fiscal Year 2012: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000); Fiscal Year 2011: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000); Fiscal Year 2010: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000); Fiscal Year 2009: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000); Fiscal Year 2008: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
• Keywords: 正準変換 / 比較原理 / 分散型方程式 / 時空間評価 / モジュレーション空間 / 波動方程式 / 平滑化効果 / シュレディンガー方程式 / 時空間評価式 / 非線形問題 / シュレデインガー方程式 / 平滑化作用 / 擬微分作用素

Research Abstract

By developing a global boundedness theory of Fourier integral operators, we established a method to deduce estimates for solutions to partial differential equations from those for their normal forms, and furthermore, prepared a new method to make a comparison of estimates for solutions from the comparison of symbols of two partial differential equations, so that we approached to nonlinear problems.

Research Products

• [Journal Article] Structural resolvent estimates and derivative nonlinear Schrodinger equations (2012)
  • Author(s): Michael Ruzhansky & Mitsuru Sugimoto
  • Journal Title: Comm. Math. Phys. Volume: 314 Pages: 281-304
  • Peer Reviewed
• [Journal Article] Smoothing properties of evolution equations via canonical transforms and comparison principle (2012)
  • Author(s): Michael Ruzhansky & Mitsuru Sugimoto
  • Journal Title: Proc. London Math. Soc. Volume: 105 Pages: 393-423
  • Peer Reviewed
• [Journal Article] Modulation Spaces and Nonlinear Evolution Equations (2012)
  • Author(s): Michael Ruzhansky, Mitsuru Sugimoto and Baoxiang Wang
  • Journal Title: Progress in Mathematics Volume: 301 Pages: 267-283
  • Peer Reviewed
• [Journal Article] Remarks on nonlinear operations on modulation spaces (2011)
  • Author(s): Mitsuru Sugimoto, Naohito Tomitaand Baoxiang Wang
  • Journal Title: Integral Transforms and Spec. Funct. Volume: 22 Pages: 351-358
  • Peer Reviewed
• [Journal Article] Weighted Sobolev L2 estimates for a class of Fourier integral operators (2011)
  • Author(s): Michael Ruzhansky & Mitsuru Sugimoto
  • Journal Title: Math. Nachr. Volume: 284 Pages: 1715-1738
  • Peer Reviewed
• [Journal Article] Mitsuru Sugimoto, Joachim Toft and Naohito Tomita, Changes of variables in modulation and Wiener amalgam spaces (2011)
  • Author(s): Michael Ruzhansky, Mitsuru Sugimoto
  • Journal Title: Math. Nachr. Volume: 284 Pages: 2078-2092
  • Peer Reviewed
• [Journal Article] The inclusion relation between Sobolev and modulation spaces (2011)
  • Author(s): Masaharu Kobayashi & Mitsuru Sugimoto
  • Journal Title: J. Funct. Anal Volume: 260 Pages: 3189-3208
  • Peer Reviewed
• [Journal Article] Remarks on nonlinear operations on modulation spaces (2011)
  • Author(s): M.Sugimoto, N.Tomita, B.Wang
  • Journal Title: Integral Transforms and Spec.Funct. Volume: 22 Pages: 351-358
  • Peer Reviewed
• [Journal Article] The inclusion relation between Sobolev and modulation spaces (2011)
  • Author(s): M.Kobayashi, M.Sugimoto
  • Journal Title: J.Funct.Anal. Volume: 260 Pages: 3189-3208
  • Peer Reviewed
• [Journal Article] Weighted Sobolev L2 estimates for a class of Fourier integral operators (2011)
  • Author(s): M.Ruzhansky, M.Sugimoto
  • Journal Title: Math.Nachr. Volume: 284 Pages: 1715-1738
  • Peer Reviewed
• [Journal Article] Changes of variables in modulatLon and Wiener amalgam spaces (2011)
  • Author(s): M.Ruzhansky, M.Sugimoto, J.Toft, N.Tomita
  • Journal Title: Math.Nachr. Volume: 284 Pages: 2078-2092
  • Peer Reviewed
• [Journal Article] Criteria for Bochner's extension problem (2010)
  • Author(s): Michael Ruzhansky & Mitsuru Sugimoto
  • Journal Title: Asymptot. Anal. Volume: 66 Pages: 125-138
  • Peer Reviewed
• [Journal Article] Motion of elastic wire with thickness (2010)
  • Author(s): Norihito Koiso & Mitsuru Sugimoto
  • Journal Title: Osaka J. Math. Volume: 47 Pages: 787-815
  • NAID: 120004840634
  • Peer Reviewed
• [Journal Article] Criteria for Bochner's extension problem (2010)
  • Author(s): M. Ruzhansky, M. Sugimoto
  • Journal Title: Asymptot.Anal 66 Pages: 125-138
  • Peer Reviewed
• [Journal Article] Motion of elastic wire with thickness (2010)
  • Author(s): N. Koiso, M. Sugimoto
  • Journal Title: OsakaJ.Math. 47 Pages: 787-815
  • NAID: 120004840634
  • Peer Reviewed
• [Journal Article] 臨界指数の重みに関する極限吸収原理とSommeribldの放射条件 (2010)
  • Author(s): 杉本充
  • Journal Title: 数理解析研究所講究録 Volume: 1696 Pages: 158-169
• [Journal Article] On the L2-boundedness of pseudo-differential operators and their commutators with symbols in α-modulation spaces (2009)
  • Author(s): Masaharu Kobayashi, Mitsuru Sugimoto & Naohito Tomita
  • Journal Title: J. Math. Anal. Appl. Volume: 350 Pages: 157-169
  • Peer Reviewed
• [Journal Article] Trace ideals for pseudo-differential operators and their commutators with symbols in α-modulation spaces (2009)
  • Author(s): Masaharu Kobayashi, Mitsuru Sugimoto & Naohito Tomita
  • Journal Title: J. Anal. Math. Volume: 107 Pages: 141-160
  • Peer Reviewed
• [Journal Article] Trace ideals for pseudo-differential operators and their commutators with symbols in α-modulation spaces (2009)
  • Author(s): M. Kobayashi, M. Sugimoto, N. Tomita
  • Journal Title: J.Anal.Math. 107 Pages: 141-160
  • Peer Reviewed
• [Journal Article] On the L^2-boundedness of pseudo-differential operators and their commutators with symbols in α-modulation spaces (2009)
  • Author(s): 杉本充, 小林政晴・冨田直人, との共著
  • Journal Title: J.Math.Anal.Appl. 350 Pages: 157-169
  • Peer Reviewed
• [Journal Article] Trace ideals for pseudo-differential operators and their commutators with symbols in α-modulation spaces (2009)
  • Author(s): 杉本充, 小林政晴・冨田直人, との共著
  • Journal Title: J.Anal.Math. 107 Pages: 141-160
  • Peer Reviewed
• [Journal Article] On the smoothing properties of dispersive partial differential equations (2009)
  • Author(s): 杉本充, M.Ruzhansky, との共著
  • Journal Title: RIMS Kokyuroku Bessatsu B14 Pages: 103-124
  • Peer Reviewed
• [Journal Article] A counterexample for boundedness of pseudo-differential operators on modulation spaces (2008)
  • Author(s): Mitsuru Sugimoto & Naohito Tomita
  • Journal Title: Proc. Amer. Math. Soc. Volume: 136 Pages: 1681-1690
  • Peer Reviewed
• [Journal Article] Boundedness properties of pseudo-differential and Calderon-Zygmund operators on modulation spaces (2008)
  • Journal Title: J. Fourier Anal. Appl. Volume: 14 Pages: 124-143
  • Peer Reviewed
• [Journal Article] A remark on fractional integrals on modulation spaces (2008)
  • Author(s): Mitsuru Sugimoto & Naohito Tomita
  • Journal Title: Math. Nachr. Volume: 281 Pages: 1372-1379
  • Peer Reviewed
• [Journal Article] Boundedness properties of pseudo-differential and Calderon-Zygmund operators on modulation spaces (2008)
  • Author(s): M. Sugimoto, N. Tomita
  • Journal Title: J.Fourier Anal.Appl. 14 Pages: 124-143
  • Peer Reviewed
• [Journal Article] A remark on fractional integrals on modulation spaces (2008)
  • Author(s): M. Sugimoto, N. Tomita
  • Journal Title: Math.Nachr. 281 Pages: 1372-1379
  • Peer Reviewed
• [Journal Article] Boundedness properties of pseudo-differential and Calderon-Zygmund operators on modulation spaces (2008)
  • Author(s): 杉本充(冨田直人との共著)
  • Journal Title: J. Fourier Anal. Appl. 14 Pages: 124-143
  • Peer Reviewed
• [Journal Article] A remark on fractional integrals on modulation spaces (2008)
  • Author(s): 杉本充(冨田直人との共著)
  • Journal Title: Math. Nachr. 281 Pages: 1372-1379
  • Peer Reviewed
• [Presentation] 「Structural resolvent estimates and derivative nonlinear Schrodinger equations 」(Plenary talk) (2012)
  • Organizer: 研究集会Al-Khorezmiy 2012
  • Place of Presentation: ウズベキスタン・ウズベキスタン国立大
  • Year and Date: 2012-12-19
• [Presentation] Optimal constants and extremisers for some smoothing estimates (2012)
  • Organizer: 研究集会Modern Methods of Time-Frequency Analysis II, Workshop "Phase space methods for pseudo-differential operators "
  • Place of Presentation: オーストリア・ESI
  • Year and Date: 2012-10-17
• [Presentation] Fourier Analysis and Pseudo-Differential Operators「Optimal constants for some smoothing estimates」 (2012)
  • Organizer: 研究集会
  • Place of Presentation: フィンランド・Aalto 大
  • Year and Date: 2012-06-25
• [Presentation] 双曲型方程式初期値問題の解の減衰評価について (2012)
  • Author(s): 杉本充
  • Organizer: CREST流体数学講演会
  • Place of Presentation: 早稲田大学理工学術院
• [Presentation] 2011 NCTS Taiwan-Japan Joint Workshop on PDEs and Geometric Analysis「A vector fields approach to smoothing and decaying estimates for equations in anisotropic media」 (2011)
  • Organizer: 研究集会
  • Place of Presentation: 台湾・NCTS
  • Year and Date: 2011-12-20
• [Presentation] A vector fields approach to smoothing and decaying estimates for equations in anisotropic media (2011)
  • Author(s): 杉本充
  • Organizer: 2011 NCTS Taiwan-Japan Joint Workshop on PDEs and Geometric Analysis
  • Place of Presentation: 台湾・NCTS
  • Year and Date: 2011-12-20
• [Presentation] A vector fields approach to smoothing and decaying estimates for equations in anisotropic media (2011)
  • Organizer: 研究集会2011 NCTS Taiwan-Japan Joint Workshop on PDEs and Geometric Analysis「A vector fields approach to smoothing and decaying estimates for equations in anisotropic media」
  • Place of Presentation: 九州大学医学部 百年講堂
  • Year and Date: 2011-09-19
• [Presentation] A vector fields approach to smoothing and decaying estimates for equations in anisotropic media (2011)
  • Author(s): 杉本充
  • Organizer: The 4th MSJ-SI "NONUNEAE DYNAMICS INPARTIAL DIFFERENTIAL EQUATIONS"
  • Place of Presentation: 九州大学医学部百年講堂
  • Year and Date: 2011-09-19
• [Presentation] Smoothing estimates for non-dispersive equations (2011)
  • Organizer: 研究集会)The 8th ISAAC Congress (Plenary talk)
  • Place of Presentation: ロシア・ロシア諸民族友好大学
  • Year and Date: 2011-08-26
• [Presentation] Smoothing estimates for non-dispersive equations (2011)
  • Author(s): 杉本充
  • Organizer: The 8th ISAAC Congres
  • Place of Presentation: ロシア・ロシア諸民族友好大学
  • Year and Date: 2011-08-26
• [Presentation] Strobl 2011 「The inclusion relation between Sobolev and modulation spaces」 (2011)
  • Organizer: 研究集会From Abstract to Computational Harmonic Analysis
  • Place of Presentation: オーストリア・シュトローブル
  • Year and Date: 2011-06-17
• [Presentation] The inclusion relation between Sobolev and modulation spaces (2011)
  • Author(s): 杉本充
  • Organizer: From Abstract to Computational Harmonic Analysis, Strobl 2011
  • Place of Presentation: オーストリア・シュトローブル
  • Year and Date: 2011-06-17
• [Presentation] Elliptic Operators and Corresponding Vector Fields (2011)
  • Organizer: 研究集会Asymptotic Properties of Solutions to Hyperbolic Equations
  • Place of Presentation: イギリス・Imperial College London
  • Year and Date: 2011-03-24
• [Presentation] Elliptic Operators and Corresponding Vector Fields (2011)
  • Organizer: 研究集会"Asymptotic Properties of Solutions to Hyperbolic Equations
  • Place of Presentation: イギリス・Imperial College London
  • Year and Date: 2011-03-24
• [Presentation] On some Lp-type estimates for evolution operators (2011)
  • Organizer: 研究集会偏微分方程式姫路研究集会
  • Place of Presentation: イーグレ姫路
  • Year and Date: 2011-02-20
• [Presentation] On some Lp-type estimates for evolution operators (2010)
  • Organizer: PDE Seminar
  • Place of Presentation: イギリス・Bath 大
  • Year and Date: 2010-12-10
• [Presentation] Smoothing estimates for dispersive and non-dispersive equations (2010)
  • Organizer: Analysis Seminar
  • Place of Presentation: イギリス・Birmingham 大
  • Year and Date: 2010-12-08
• [Presentation] Microlocal Day #2 「On some Lp-type estimates for evolution operators」 (2010)
  • Organizer: 研究集会
  • Place of Presentation: イギリス・Imperial College London
  • Year and Date: 2010-12-03
• [Presentation] Smoothing estimates for dispersive and non-dispersive equations (2010)
  • Organizer: 研究集会2010 Workshop on Fourier Analysis and Its Applications to PDEs
  • Place of Presentation: 湾・NCTS
  • Year and Date: 2010-07-01
• [Presentation] Smoothing estimates for dispersive and non-dispersive equations (2010)
  • Author(s): 杉本充
  • Organizer: 2010 Workshop on Fourier Analysis and Its Applications to PDEs
  • Place of Presentation: 台湾・NCTS
  • Year and Date: 2010-07-01
• [Presentation] Smoothing estimates for dispersive and non-dispersive equations (2009)
  • Organizer: 研究集会International Conference on Generalized Functions GF2009- (Plenary talk)
  • Place of Presentation: オーストリア・ウィーン大学
  • Year and Date: 2009-09-01
• [Presentation] Smoothing estimates for dispersive and non-dispersive equations (2009)
  • Organizer: 研究集会"International Conference on Generalized Functions GF2009"
  • Place of Presentation: オーストリア・ウィーン大学
  • Year and Date: 2009-09-01
• [Presentation] Smoothing estimates for dispersive and non-dispersive equations (2009)
  • Organizer: 研究集会Nonlinear PDE in Zhang Jia Jie
  • Place of Presentation: 中国・張家界
  • Year and Date: 2009-08-11
• [Presentation] 発展方程式に対する平滑化評価式について (2009)
  • Organizer: 第48回実函数論・関数解析学合同シンポジウム
  • Place of Presentation: 松本市 松本中央公民館
  • Year and Date: 2009-08-07
• [Presentation] Limiting absorption principle in the critical case and Sommerfeld radiation condition (2009)
  • Organizer: セミナー
  • Place of Presentation: 中国・北京大学
  • Year and Date: 2009-05-30
• [Presentation] Space-time estimates for evolution equations via comparison (2009)
  • Organizer: 研究集会Harmonic Analysis and Partial Differential Equations with Applications
  • Place of Presentation: 中国・北京師範大学
  • Year and Date: 2009-05-30
• [Presentation] 分散型方程式の時空間評価式と比較原理(特別講演) (2009)
  • Organizer: 日本数学会年会 函数方程式論分科会
  • Place of Presentation: 東京大
  • Year and Date: 2009-03-27
• [Presentation] 分散型方程式の時空間評価式と比較原理 (2009)
  • Organizer: 日本数学会2009年度年会函数方程式論分科会特別講演
  • Place of Presentation: 東京大
  • Year and Date: 2009-03-27
• [Presentation] 分散型方程式の時空間評価式と比較原理 (2009)
  • Author(s): 杉本充
  • Organizer: 日本数学会2009年度年会函数方程式論分科会特別講演
  • Place of Presentation: 東京大学
  • Year and Date: 2009-03-27
• [Presentation] Limiting absorption principle in the critical case and Sommerfeld radiation condition (2009)
  • Organizer: 研究集会第26回九州における偏微分方程式研究集会
  • Place of Presentation: 九州大学
  • Year and Date: 2009-01-28
• [Presentation] A limiting absorption principle in the critical case and a radiation condition (2008)
  • Organizer: 研究集会Linear and Nonlinear Waves, No.6
  • Place of Presentation: ピアザ淡海 滋賀県立県民交流センター
  • Year and Date: 2008-12-10
• [Presentation] Limiting absorption principle in the critical case and Sommerfeld radiation condition (2008)
  • Organizer: 研究集会PDEs and Function Spaces / London Analysis and Probability Seminar
  • Place of Presentation: イギリス・Imperial College London
  • Year and Date: 2008-12-04
• [Presentation] A limiting absorption principle in the critical case and a radiation condition (2008)
  • Organizer: 研究集会Decay and Regularity for Solutions of Differential Equations and Dynamical systems
  • Place of Presentation: イタリア・Cagliari 大学
  • Year and Date: 2008-09-25
• [Presentation] A limiting absorption principle in the critical case and a radiation condition (2008)
  • Organizer: 研究集会International Conference on Partial Differential Equations and Spectral Theory
  • Place of Presentation: ドイツ・ゴスラー
  • Year and Date: 2008-09-05
• [Presentation] A limiting absorption principle in the critical case and a radiation condition (2008)
  • Organizer: 研究集会"International Conference on Partial Differential Equations and Spectral Theory
  • Place of Presentation: ドイツ・ゴスラー
  • Year and Date: 2008-09-05
• [Presentation] Smoothing estimates for dispersive equations via canonical transforms and comparison principle (2008)
  • Organizer: 研究集会Pseudo-differential Operators and Related Topics, II
  • Place of Presentation: スウェーデン・Vaxjo 大学
  • Year and Date: 2008-06-23
• [Presentation] Smoothing estimates for dispersive equations via canonical transforms and comparison principle (2008)
  • Organizer: 研究集会"Pseudo-differential Operators and Related Topics, II"
  • Place of Presentation: スウェーデン・Vaxjo大学
  • Year and Date: 2008-06-23
• [Presentation] Optimal constants for some smoothing estimates
  • Author(s): Mitsuru Sugimoto
  • Organizer: The international conference “Fourier Analysis and Pseudo-Differential Operators”
  • Place of Presentation: フィンランド・Aalto 大
  • Invited
• [Presentation] Optimal constants and extremisers for some smoothing estimates
  • Author(s): Mitsuru Sugimoto
  • Organizer: Workshop “Phase space methods for pseudo-differential operators”
  • Place of Presentation: オーストリア・ESI
  • Invited
• [Presentation] Modern problems of applied mathematics and information technologies - Al-Khorezmiy 2012
  • Author(s): Mitsuru Sugimoto
  • Organizer: Structural resolvent estimates and derivative nonlinear Schrodinger equations
  • Place of Presentation: ウズベキスタン・ウズベキスタン国立大
  • Invited
• [Book] 日本の現代数学 -新しい展開をめざして (2010)
  • Author(s): 小川卓克・斎藤 毅・中島 啓
  • Total Pages: 256
  • Publisher: 数学書房
• [Book] 日本の現代数学-新しい展開をめざして (2010)
  • Author(s): 小川卓克・斎藤毅・中島啓編
  • Total Pages: 256
  • Publisher: 数学書房
• [Book] 「日本の現代数学-新しい展開をめざして」小川卓克・斎藤毅・中島啓編 (2010)
  • Author(s): 杉本充, 他11名との共同執筆
  • Total Pages: 256
  • Publisher: 数学書房
• [Book] プリンストン解析学講義2「複素解析」エリアス・M.スタイン,ラミ・シャカルチ (2009)
  • Author(s): 訳書(新井仁之,高木啓行,千原浩之との共訳)
  • Total Pages: 404
  • Publisher: 日本評論社
• [Book] 複素解析(新井仁之,高木啓行,千原浩之との共訳)プリンストン解析学講義2 訳書 (2009)
  • Author(s): エリアス・M.スタイン,ラミ・シャカルチ著
  • Total Pages: 404
  • Publisher: 日本評論社
• [Book] プリンストン解析学講義2「複素解析」エリアス・M. スタイン, ラミ・シャカルチ著 (2009)
  • Author(s): 杉本充, 新井仁之, 高木啓行, 千原浩之, との共訳
  • Total Pages: 404
  • Publisher: 日本評論社
• [Remarks]
  • URL: http://www.math.nagoya-u.ac.jp/~sugimoto/
• [Remarks]
  • URL: http://www.math.nagoya-u.ac.jp/~sugimoto/
• [Remarks] ホームページ
  • URL: http://www.math.nagoya-u.ac.jp/~sugimoto/
• [Remarks]
  • URL: http://www.math.nagoya-u.ac.jp/_sugimoto/
• [Remarks]
  • URL: http://www.math.nagoya-u.ac.jp/~sugimoto/