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On a spectral theory for operators with dissipative terms

Research Project

Project/Area Number 20540187
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionGakushuin University

Principal Investigator

WATANABE Kazuo  Gakushuin University, 理学部, 助教 (90260851)

Co-Investigator(Kenkyū-buntansha) 門脇 光輝  愛媛大, 理工学研究科, 教授 (70300548)
中澤 秀夫  千葉工業大学, 工学部, 准教授 (80383371)
Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords非自己共役 / 消散項 / スペクトル理論 / Maxwell方程式 / 自己共役性 / 波動作用素 / 散乱作用素 / 正則性 / スペクトル / 散乱 / 波動方程式 / 消散
Research Abstract

Kadowaki, Nakazawa and Watanabe have studied for the properties of the wave operators with dissipative terms. In the case of the short range perturbations, we proved the existence of the wave operators. In the case of the long range perturbations, the energy of all solutions decays at infinity. The results appeared in Electric Journal of Differential Equation (April 2011). Watanabe studied the interface regularity of the solution for : the rotation system, the self-interactive system (MHD).

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (61 results)

All 2011 2010 2009 2008 Other

All Journal Article (13 results) (of which Peer Reviewed: 6 results) Presentation (47 results) Remarks (1 results)

  • [Journal Article] On wave equations with dissipation II2010

    • Author(s)
      中澤秀夫
    • Journal Title

      Rend.Instit.Mat.Univ.Trieste vol.45

      Pages: 165-184

    • Related Report
      2010 Final Research Report
  • [Journal Article] On wave equations with dissipation II.2010

    • Author(s)
      中澤秀夫
    • Journal Title

      Rend.Istit.Mat.Univ.Trieste

      Volume: 42 Pages: 165-184

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An aspect for spectral analysis of non-selfadjoint operators : Schr\"odinger and wave equations2009

    • Author(s)
      中澤秀夫
    • Journal Title

      MI Lecture Note Series vol.20

      Pages: 115-136

    • Related Report
      2010 Final Research Report
  • [Journal Article] On the rank one dissipative operator and the Parseval formula2009

    • Author(s)
      門脇光輝, 中澤秀夫, 渡邊一雄
    • Journal Title

      Operator Theory : Advances and Applications vol.186

      Pages: 241-256

    • Related Report
      2010 Final Research Report
  • [Journal Article] 非自己共役作用素のスペクトル構造の解明と散乱理論および逆問題に関する研究2009

    • Author(s)
      中澤秀夫
    • Journal Title

      千葉工業大学プロジェクト研究年報 vol.6

      Pages: 175-176

    • Related Report
      2010 Final Research Report
  • [Journal Article] Some results on spectral analysis of nonselfadjoint perturbations for Schrodinger and wave \par equations2009

    • Author(s)
      門脇光輝, 中澤秀夫, 渡邊一雄
    • Journal Title

      Begehr, H. G. W. (ed.) et al., Further progress in analysis. Proceedings of the 6th international ISAAC congress

      Pages: 465-475

    • Related Report
      2010 Final Research Report
  • [Journal Article] An aspect for spectral analysis of non-selfadjoint operators : Schr¥" odinger and wave equations.2009

    • Author(s)
      中澤秀夫
    • Journal Title

      MI Lecture Note Series

      Volume: 20 Pages: 115-136

    • Related Report
      2009 Annual Research Report
  • [Journal Article] 非自己共役作用素のスペクトル構造の解明と散乱理論および逆問題に関する研究2009

    • Author(s)
      中澤秀夫
    • Journal Title

      千葉工業大学プロジェクト研究年報

      Volume: 6 Pages: 175-176

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Some results on spectral analysis of nonselfadjoint perturbations for Schrodinger and wave ¥par equations.2009

    • Author(s)
      中澤秀夫
    • Journal Title

      Begehr, H.G.W.(ed.) et al., Further progress in analysis. Proceedings of the 6th international ISAAC congress

      Pages: 465-475

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the rank one dissipative operator and the Parseval formula.2009

    • Author(s)
      渡辺一雄
    • Journal Title

      Operator Theory : Advances and Applications

      Volume: 186 Pages: 241-256

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some results on spectral analysis of nonselfadjoint Perturbation for Schroedinger and wave equations2009

    • Author(s)
      M. Kadowaki, H. Nakazawa And K. Watanabe
    • Journal Title

      Further Progress in Analysis, Proc. 6^<th> int. ISAAC Congress

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the rank one operator and the Parseval formula2008

    • Author(s)
      M. Kadowaki, H. Nakazwa, K. Watanabe
    • Journal Title

      Methods of Spectral Anal. and Op. Th. in Math. Phys., OTAMP 2006 Lund

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Parseval formula for the wave equations with dissipative terms of rank one2008

    • Author(s)
      M. Kadowaki, H. Nakazwa, K. Watanabe
    • Journal Title

      SUT Jour. Math. 44

    • NAID

      120006397990

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Mourre estimateについての解説2011

    • Author(s)
      渡邊一雄
    • Organizer
      解析学研究セミナー
    • Place of Presentation
      学習院大学
    • Year and Date
      2011-01-15
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 放射条件に関連するHardy型不等式と2次元外部領域におけHelmholtz方程式のresolvent評価2011

    • Author(s)
      中澤秀夫
    • Organizer
      日本数学会春期年会
    • Place of Presentation
      早稲田大学
    • Related Report
      2010 Final Research Report
  • [Presentation] 放射条件に関連するHardy型不等式と2次元外部領域におけHelmholtz方程式のresolvent評価2011

    • Author(s)
      中澤秀夫
    • Organizer
      日本数学会秋季年会
    • Place of Presentation
      早稲田大学
    • Related Report
      2010 Annual Research Report
  • [Presentation] Asymptotic observableについての解説2010

    • Author(s)
      渡邊一雄
    • Organizer
      解析学研究セミナー
    • Place of Presentation
      学習院大学
    • Year and Date
      2010-12-08
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 3次元半空間の波動伝播と定常位相の方法について2010

    • Author(s)
      門脇光輝
    • Organizer
      信州松本偏微分方程式セミナー
    • Place of Presentation
      松本市中央公民館Mウィング南
    • Year and Date
      2010-12-04
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 渦なし系の階の界面正則性2010

    • Author(s)
      渡邊一雄
    • Organizer
      研究集会「数理物理と微分方程式」
    • Place of Presentation
      かんぽの宿修善寺
    • Year and Date
      2010-11-07
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 2次元外部領域におけるHELMHOLTZ方程式のRESOLVENT 評価とその応用2010

    • Author(s)
      中澤秀夫
    • Organizer
      3大学偏微分方程式セミナー
    • Place of Presentation
      国士舘大学
    • Year and Date
      2010-10-27
    • Related Report
      2010 Final Research Report
  • [Presentation] 2次元外部領域におけるHELMHOLTZ方程式のRESOLVENT評価とその応用2010

    • Author(s)
      中澤秀夫
    • Organizer
      3大学偏微分方程式セミナー
    • Place of Presentation
      国士舘大学
    • Year and Date
      2010-10-27
    • Related Report
      2010 Annual Research Report
  • [Presentation] 2次元外部領域におけるHELMHOLTZ方程式のRESOLVENT 評価とその応用2010

    • Author(s)
      中澤秀夫
    • Organizer
      新潟偏微分方程式研究集会
    • Place of Presentation
      新潟大学
    • Year and Date
      2010-10-11
    • Related Report
      2010 Final Research Report
  • [Presentation] 2次元外部領域におけるHELMHOLTZ方程式のRESOLVENT評価とその応用2010

    • Author(s)
      中澤秀夫
    • Organizer
      新潟偏微分方程式研究集会
    • Place of Presentation
      新潟大学
    • Year and Date
      2010-10-11
    • Related Report
      2010 Annual Research Report
  • [Presentation] Interface regularity of the solutions for the divergence or rotation free system2010

    • Author(s)
      渡邊一雄
    • Organizer
      新潟偏微分方程式研究集会
    • Place of Presentation
      新潟大学駅南キャンパス
    • Year and Date
      2010-10-10
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Yafaevの定式化による散乱理論2010

    • Author(s)
      門脇光輝
    • Organizer
      新潟偏微分方程式研究集会
    • Place of Presentation
      新潟大学南キャンパス
    • Year and Date
      2010-10-10
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 2次元外部領域におけるHELMHOLTZ方程式のRESOLVENT評価とその応用2010

    • Author(s)
      中澤秀夫
    • Organizer
      解析学研究セミナー
    • Place of Presentation
      学習院大学
    • Year and Date
      2010-10-02
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Lax-PhillipsとEnssの方法について2010

    • Author(s)
      門脇光輝
    • Organizer
      作用素論シンポジウム
    • Place of Presentation
      松本市中央公民館Mウィング南
    • Year and Date
      2010-09-04
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Several topics on wave equations with dissipation2010

    • Author(s)
      中澤秀夫
    • Organizer
      Operator Theory and Mathematical Physics
    • Place of Presentation
      ポーランド(Bedlow)
    • Year and Date
      2010-08-12
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Interface regularity of the solutions for the divergence or rotation free system2010

    • Author(s)
      渡邊一雄
    • Organizer
      Operator Theory and Mathematical Physics
    • Place of Presentation
      ポーランド(Bedlow)
    • Year and Date
      2010-08-09
    • Related Report
      2010 Annual Research Report 2010 Final Research Report 2009 Annual Research Report
  • [Presentation] ピストンピン型物体の断面外周の再構成2010

    • Author(s)
      門脇光輝
    • Organizer
      教育研究コロキューム
    • Place of Presentation
      都立産業技術高専荒川キャンパス
    • Year and Date
      2010-07-02
    • Related Report
      2010 Final Research Report
  • [Presentation] ピストンピン型物体の断面外周の再構成2010

    • Author(s)
      門脇光輝
    • Organizer
      教育研究コロキューム
    • Place of Presentation
      立産業技術高専荒川キャンパス
    • Year and Date
      2010-07-02
    • Related Report
      2010 Annual Research Report
  • [Presentation] Navier-Stokes方程式の解の存在について2010

    • Author(s)
      渡邊一雄
    • Organizer
      解析学研究セミナー
    • Place of Presentation
      学習院大学
    • Year and Date
      2010-06-12
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Compactness theoremについて2010

    • Author(s)
      渡邊一雄
    • Organizer
      解析学研究セミナー
    • Place of Presentation
      学習院大学
    • Year and Date
      2010-05-29
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 放射条件に関連するHardy型不等式と2次元外部領域におけHelmholtz方程式のresolvent評価2010

    • Author(s)
      中澤秀夫
    • Organizer
      愛媛大学解析セミナー
    • Place of Presentation
      愛媛大学
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Stokes方程式の解の正則性について2009

    • Author(s)
      渡邊一雄
    • Organizer
      解析学研究セミナー
    • Place of Presentation
      学習院大学
    • Year and Date
      2009-12-05
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] 国際研究集会にて座長を行った2009

    • Author(s)
      渡邊一雄
    • Organizer
      現象解析と関数方程式の新展望
    • Place of Presentation
      京大数理研
    • Year and Date
      2009-11-16
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] 2次元のラプラシアンについて2009

    • Author(s)
      渡邊一雄
    • Organizer
      研究集会「数理物理と微分方程式」
    • Place of Presentation
      かんぽの宿焼津
    • Year and Date
      2009-11-04
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] 3次元半空間における弾性波のレゾルベントについて2009

    • Author(s)
      門脇光輝
    • Organizer
      八王子偏微分方程式研究集会
    • Place of Presentation
      八王子セミナーハウス
    • Year and Date
      2009-10-10
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] 2次元平行平板間における波動伝播とその数値計算2009

    • Author(s)
      門脇光輝
    • Organizer
      第3回数物研究会
    • Place of Presentation
      キャンパスプラザ京都
    • Year and Date
      2009-09-29
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] レゾルベントの漸近挙動とその証明について2009

    • Author(s)
      門脇光輝
    • Organizer
      2009夏の作用素論シンポジュウム
    • Place of Presentation
      いわて県民情報交流センターアイーナ
    • Year and Date
      2009-09-06
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] Decay and scattering for wave equations with dissipations in layered media2009

    • Author(s)
      中澤秀夫
    • Organizer
      7th ISAAC Congress International Society for Analysis, its Applications and Computation
    • Place of Presentation
      Imperial college of London(England)
    • Year and Date
      2009-07-15
    • Related Report
      2010 Final Research Report
  • [Presentation] Decay and scattering for wave equations with dissipations in layered media2009

    • Author(s)
      中澤秀夫
    • Organizer
      7th ISAAC Congress International Society for Analysis, its Applications and Computation
    • Place of Presentation
      Imperial college of London (England)
    • Year and Date
      2009-07-15
    • Related Report
      2009 Annual Research Report
  • [Presentation] On scattering for wave equations with dissipative terms in layered media2009

    • Author(s)
      門脇光輝
    • Organizer
      2009年春季数学会
    • Place of Presentation
      東京大学駒場キャンパス
    • Year and Date
      2009-03-26
    • Related Report
      2010 Final Research Report
  • [Presentation] On scattering for wave equations with dissipative terms In the layered media2009

    • Author(s)
      門脇 光輝
    • Organizer
      2009年春期日本数学会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-26
    • Related Report
      2008 Annual Research Report
  • [Presentation] An aspect for spectral analysis of non-selfadjoint operators-Schrodinger and wave equations-2009

    • Author(s)
      中澤秀夫
    • Organizer
      産業技術数理チュートリアル:非エルミート作用素のスペクトル理論とその応用
    • Place of Presentation
      九州大学箱崎キャンパス理学部本館
    • Year and Date
      2009-03-20
    • Related Report
      2010 Final Research Report
  • [Presentation] An aspect for spectral analysis of non-selfadjoint operators -Schroedinger and wave equations-2009

    • Author(s)
      中澤 秀夫
    • Organizer
      産業技術チュートリアル, 非エルミート作用素のスペクトル理論とその応用
    • Place of Presentation
      九州大学
    • Year and Date
      2009-03-20
    • Related Report
      2008 Annual Research Report
  • [Presentation] 帯状領域における消散項を持つ波動方程式について2009

    • Author(s)
      渡辺一雄
    • Organizer
      研究集会第19回「微分方程式と数理物理」
    • Place of Presentation
      ウエルハートピア熱海(静岡)
    • Year and Date
      2009-03-17
    • Related Report
      2010 Final Research Report
  • [Presentation] On scattering for wave equations with dissipative terms in layered media(その1)2009

    • Author(s)
      中澤秀夫
    • Organizer
      望月清先生退職記念研究集会
    • Place of Presentation
      中央大学理工学部
    • Year and Date
      2009-03-17
    • Related Report
      2010 Final Research Report
  • [Presentation] On scattering for wave equations with dissipative terms In the layered media I2009

    • Author(s)
      門脇 光輝
    • Organizer
      望月清先生退職記念研究集会
    • Place of Presentation
      中央大学
    • Year and Date
      2009-03-17
    • Related Report
      2008 Annual Research Report
  • [Presentation] On scattering for wave equations with dissipative terms In the layered media II2009

    • Author(s)
      中澤 秀夫
    • Organizer
      望月清先生退職記念研究集会
    • Place of Presentation
      中央大学
    • Year and Date
      2009-03-17
    • Related Report
      2008 Annual Research Report
  • [Presentation] ピストンピン型物体の断面外周の再構成2008

    • Author(s)
      門脇光輝
    • Organizer
      第2回数物研究会
    • Place of Presentation
      富山大学理学部
    • Year and Date
      2008-12-12
    • Related Report
      2010 Final Research Report
  • [Presentation] ピストンピン型物体の断面外周の再構成2008

    • Author(s)
      門脇 光輝
    • Organizer
      第二回数物研究会
    • Place of Presentation
      富山大学
    • Year and Date
      2008-12-12
    • Related Report
      2008 Annual Research Report
  • [Presentation] 帯状領域での消散波動の散乱問題とLax-Phillips的な証明について2008

    • Author(s)
      門脇光輝
    • Organizer
      米子偏微分方程式研究集会
    • Place of Presentation
      米子高専
    • Year and Date
      2008-10-11
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Presentation] 帯状領域での消散波動の散乱問題とLax-Phillips的な証明について2008

    • Author(s)
      門脇光輝
    • Organizer
      数理科学セミナー
    • Place of Presentation
      キャンパスポート大阪
    • Year and Date
      2008-09-03
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Presentation] Wave equation on the strip domain2008

    • Author(s)
      渡邊一雄
    • Organizer
      Operator Theory, Analysis and Mathematical Physics
    • Place of Presentation
      Bedlowo(Poland)
    • Year and Date
      2008-06-21
    • Related Report
      2010 Final Research Report
  • [Presentation] Wave equation in the strip domain2008

    • Author(s)
      Kazuo Watanabe
    • Organizer
      Op. Th. And Math. Phys.
    • Place of Presentation
      Bedlowo (Poland)
    • Year and Date
      2008-06-21
    • Related Report
      2008 Annual Research Report
  • [Presentation] On scattering for wave equations with dissipative terms in layered media2008

    • Author(s)
      門脇光輝
    • Organizer
      広島数理解析セミナー
    • Place of Presentation
      広島大学
    • Year and Date
      2008-06-20
    • Related Report
      2010 Final Research Report
  • [Presentation] On scattering for wave equations with dissipative terms In the layered media2008

    • Author(s)
      門脇 光輝
    • Organizer
      広島数理解析セミナー
    • Place of Presentation
      広島大学
    • Year and Date
      2008-06-20
    • Related Report
      2008 Annual Research Report
  • [Presentation] 微分幾何入門(5)2008

    • Author(s)
      渡辺一雄
    • Organizer
      第5回解析学研究セミナー
    • Place of Presentation
      学習院大学
    • Year and Date
      2008-05-17
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Presentation] 微分幾何入門(4)2008

    • Author(s)
      渡辺一雄
    • Organizer
      第4回解析学研究セミナー
    • Place of Presentation
      学習院大学
    • Year and Date
      2008-04-12
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Remarks] ホームページ等

    • Related Report
      2010 Final Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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