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Research on Schroedinger equations by wave packet transform

Research Project

Project/Area Number 25400183
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Mathematical analysis
Research InstitutionTokyo University of Science

Principal Investigator

Kato Keiichi  東京理科大学, 理学部, 教授 (50224499)

Co-Investigator(Renkei-kenkyūsha) Ito Shingo  北里大学, 一般教育, 教授 (40548145)
Kobayashi Masaharu  北海道大学, 大学院理学研究科, 准教授 (30516480)
Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Keywords波束変換 / Wave packet transform / Schroedinger equation / Modulation space / Wave front set / Harmonic oscillator / シュレーディンガー方程式 / 波面集合 / 変調空間 / 波動作用素 / Wave operator
Outline of Final Research Achievements

By using the representation of solutions to Schroedinger equations in terms of wave packet transform given by the representative of this research project and the co-workers, the representative and the co-workers has studied properties of solutions to Schroedinger equations. More precisely, we have characterize singularities to Schroedinger equations with time dependent sub-quadratic potentials and for purturbed harmonic oscillator in terms of information of
initial data.
We have studied existence and completeness of wave operators for Schroedinger equations with time dependent potentials. We have shown existence and completeness of wave operator for Schroedinger equations with time dependent shortrange potentials.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (23 results)

All 2016 2015 2014 2013 Other

All Journal Article (6 results) (of which Peer Reviewed: 6 results,  Open Access: 2 results) Presentation (17 results) (of which Int'l Joint Research: 2 results,  Invited: 15 results)

  • [Journal Article] Local and global solvability and blow up for the drift-diffusion equation with the fractional dissipation with the critical space2015

    • Author(s)
      Sugiyama, Y., Yamamoto, M., Kato, K.
    • Journal Title

      Journal of Differential Equations

      Volume: 258 Issue: 9 Pages: 2983-3010

    • DOI

      10.1016/j.jde.2014.12.033

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Wave front set defined by wave packet transform and its application2015

    • Author(s)
      Keiichi Kato, Masaharu Kobayashi and Shingo Ito
    • Journal Title

      Adv. Stud. Pure Math.

      Volume: 64 Pages: 417-425

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence and analyticity of solutions to the drift-diffusion equation with critical dissipation2014

    • Author(s)
      Masakazu Yamamoto, Keiichi Kato and Yuusuke Sugiyama
    • Journal Title

      Hiroshima Mathmatical Journal

      Volume: 44 Pages: 275-313

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Singularities for solutions to time dependent Schroedinger equations with sub-quadratic potential2014

    • Author(s)
      Keiichi Kato and Shingo Ito
    • Journal Title

      SUT Journal of Mathematics

      Volume: 50 Pages: 383-398

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Estimates on modulation spaces for Schr\"odinger evolution operators with quadratic and sub-quadratic potentials2014

    • Author(s)
      K.Kato, M.Kobayashi, S.Ito
    • Journal Title

      J. Funct. Anal.

      Volume: 266 Issue: 2 Pages: 733-753

    • DOI

      10.1016/j.jfa.2013.08.017

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Charcterization of wave front sets in Fourier-Lebesgue spaces and its applications2013

    • Author(s)
      Keiichi Kato, Masaharu Kobayashi and Shingo Ito
    • Journal Title

      Funkcialaj Ekvacioj

      Volume: 56 Pages: 1-17

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] Wave packet transform and singularities of solutions to Schroedinger equations2016

    • Author(s)
      加藤圭一
    • Organizer
      International conference on partial differential equations
    • Place of Presentation
      中国金華市浙江師範大学
    • Year and Date
      2016-03-25
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 波束変換の分散型方程式への応用2016

    • Author(s)
      加藤圭一
    • Organizer
      松山解析セミナー2016
    • Place of Presentation
      愛媛大学理学部
    • Year and Date
      2016-02-05
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] 波面集合の特徴付けについて2015

    • Author(s)
      伊藤真吾,加藤圭一
    • Organizer
      第54回実函数論・函数解析学合同シンポジウム
    • Place of Presentation
      神奈川大学
    • Year and Date
      2015-09-03
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Wave packet transform and its application to partial differential equations2015

    • Author(s)
      加藤圭一
    • Organizer
      nonlinear PDE meeting at Yanbian University
    • Place of Presentation
      中国延吉市延辺大学
    • Year and Date
      2015-07-07
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Wave packet transform and Schroedinger equations with time dependent potentials2015

    • Author(s)
      加藤圭一
    • Organizer
      Workshop on nonlinear paratial differential equations
    • Place of Presentation
      Zhejian University, China
    • Year and Date
      2015-03-14 – 2015-03-15
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Wave packet transform and its application to Schroedinger operators2015

    • Author(s)
      加藤圭一
    • Organizer
      第7回名古屋微分方程式研究集会
    • Place of Presentation
      名古屋大学大学院多元数理研究科
    • Year and Date
      2015-03-03 – 2015-03-05
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Existence and completeness of the wave operator for Schroedinger equations with time dependent short range potentials via wave packet transform2015

    • Author(s)
      米山泰祐(発表代表者) ,加藤圭一
    • Organizer
      Critical Exponents and Nonlinear Evolution Equation 2015
    • Place of Presentation
      東京理科大学神楽坂キャンパス
    • Year and Date
      2015-02-20 – 2015-02-21
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 波束変換とシュレディンガー方程式の解の特異性2015

    • Author(s)
      加藤圭一
    • Organizer
      第1回解析学の耳袋
    • Place of Presentation
      プラザヴェルデ(沼津)
    • Year and Date
      2015-01-14 – 2015-01-16
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 波束変換と偏微分方程式の解の特異性2014

    • Author(s)
      加藤圭一
    • Organizer
      大阪大学理学部数学教室微分方程式セミナー
    • Place of Presentation
      大阪大学理学部
    • Year and Date
      2014-12-05
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 双曲型方程式の特異性伝播と波束変換2014

    • Author(s)
      加藤圭一
    • Organizer
      第25回数理物理と微分方程式
    • Place of Presentation
      強羅静雲荘
    • Year and Date
      2014-11-01 – 2014-11-03
    • Related Report
      2014 Research-status Report
  • [Presentation] 波束変換の偏微分方程式への応用2014

    • Author(s)
      加藤圭一
    • Organizer
      第4回室蘭非線形解析研究会
    • Place of Presentation
      室蘭工業大学
    • Year and Date
      2014-10-17 – 2014-10-18
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 波束変換による波面集合の特徴づけについて2014

    • Author(s)
      伊藤真吾(発表代表者),加藤圭一
    • Organizer
      神楽坂解析セミナー
    • Place of Presentation
      東京理科大学神楽坂キャンパス
    • Year and Date
      2014-07-26
    • Related Report
      2014 Research-status Report
  • [Presentation] Characterization of Wave front set via wave packet transform2014

    • Author(s)
      加藤圭一
    • Organizer
      秋田における偏微分方程式集中ワークショップ
    • Place of Presentation
      秋田大学教育文化学部
    • Year and Date
      2014-07-12
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 波束変換とそのシュレーディンガー方程式への応用2014

    • Author(s)
      加藤圭一
    • Organizer
      函館における偏微分方程式論集中ワークショップ
    • Place of Presentation
      はこだて未来大学
    • Year and Date
      2014-04-05 – 2014-04-06
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] stimates on modulation spaces for Schroedinger evolution operators with quadratic and sub-quadratic potentials

    • Author(s)
      Shingo Ito
    • Organizer
      日本数学会関数方程式論分科会「微分方程式の総合的研究」
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Application of wave packet transformation to time-dependent Schroedinger equation

    • Author(s)
      Keiichi Kato
    • Organizer
      RIMS研究集会「スペクトル散乱理論とその周辺」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Wave packet transform and its application for PDE

    • Author(s)
      Keiichi Kato
    • Organizer
      Workshop "Harmonic analysis for nonlinear problems in UCSB
    • Place of Presentation
      University of California Santa Barbara
    • Related Report
      2013 Research-status Report
    • Invited

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Published: 2014-07-25   Modified: 2019-07-29  

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