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Spectral analysis of elliptic operators with singular domain deformation and coefficients degeneration

Research Project

Project/Area Number 17340042
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionHokkaido University

Principal Investigator

JIMBO Shuichi  Hokkaido University, 大学院・理学研究院, 教授 (80201565)

Co-Investigator(Kenkyū-buntansha) NAKAMURA Gen  北海道大学, 大学院・理学研究院, 教授 (50118535)
TACHIZAWA Kazuya  北海道大学, 大学院・理学研究院, 准教授 (80227090)
HONDA Naofumi  北海道大学, 大学院・理学研究院, 准教授 (00238817)
森田 善久  龍谷大学, 理工学部, 教授 (10192783)
倉田 和浩  首都大学東京, 大学院・理工学研究科, 教授 (10186489)
Project Period (FY) 2005 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥17,240,000 (Direct Cost: ¥14,900,000、Indirect Cost: ¥2,340,000)
Fiscal Year 2008: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2007: ¥5,720,000 (Direct Cost: ¥4,400,000、Indirect Cost: ¥1,320,000)
Fiscal Year 2006: ¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2005: ¥3,800,000 (Direct Cost: ¥3,800,000)
Keywords細い弾性体 / 振動数 / 摂動解析 / GL方程式 / 8の字型超伝導体 / 分岐構造 / 楕円型作用素 / 特異摂動問題 / 領域変形 / ラメ作用素 / 固有値 / 摂動公式 / 半古典近似 / 固有振動 / 特異摂動 / 楕円形作用素 / 固有値問題 / 変分問題
Research Abstract

1. 典型的な2階楕円型作用素において, 特異的な領域変形の過程あるいは変数係数が特異摂動を受ける過程において, 固有値の漸近挙動を解析した. 扱った作用素はラプラス作用素, ラメ作用素, マクスウェルの作用素シュレディンガー作用素などである.
2. ジャンクションをもつ集合上のギンツブルク-ランダウ方程式の解構造を解析した. 分岐や安定性を調べた.

Report

(5 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (77 results)

All 2009 2008 2007 2006 2005 Other

All Journal Article (36 results) (of which Peer Reviewed: 24 results) Presentation (37 results) Book (4 results)

  • [Journal Article] Ginzburg-Landau equation and solution structure2008

    • Author(s)
      S. Jimbo, Y. Morita
    • Journal Title

      Sugaku Expositions 21

      Pages: 117-131

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Inverse analysis for magnetic resonance elastography2008

    • Author(s)
      G. Nakamura, Y. Jian, S. Nagayasu, J. Cheng
    • Journal Title

      Applicable Analysis 87

      Pages: 165-179

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] The non-response approach and its relation to non-iterative methods for the inverse scattering2008

    • Author(s)
      N. Honda, R. Potthast, G. Nakamura, M. Sini
    • Journal Title

      Ann. Mat. Pure Appl 87

      Pages: 7-37

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] The geometric structure of a virtual turning point of the model of the Stokes geometry2008

    • Author(s)
      N. Honda
    • Journal Title

      RIMS kokyuroku Bessatsu B10

      Pages: 63-113

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Principally tame regular sequences associated with the Fourth Painleve hierarchy with a parameter Proc2008

    • Author(s)
      N. Honda, T. Aoki
    • Journal Title

      Japan Acad 84

      Pages: 42-47

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Wavelet characterizations of weighted Herz spaces Scientiae Mathematicae Japonicae2008

    • Author(s)
      M. Izuki, and K. Tachizawa
    • Journal Title

      67

      Pages: 353-363

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Unique continuation for the elastic transversely isotropic dynamical systems and its application2008

    • Author(s)
      C. L. Lin, G. Nakamura, M. Sini
    • Journal Title

      J. Differential Equations 245

      Pages: 3008-3024

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Inversion analysis for magnetic resonance elastography2008

    • Author(s)
      G. Nakamura,Y. Jiang, S. Nagayasu, Sei, J. Cheng
    • Journal Title

      Appl. Anal 87

      Pages: 165-179

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Ginzburg-Landau equations and solutions structure2008

    • Author(s)
      S. Jimbo, Y. Morita
    • Journal Title

      Sugaku Expositions 21

      Pages: 117-131

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Inverse analysis for magnetic resonance elastography2008

    • Author(s)
      G. Nakamura, Y. Jiang, S. Nagayasu, J. Cheng
    • Journal Title

      Applicable Analysis 87

      Pages: 165-179

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The no-response approach and its relationto non-iterative methods for the inverse scattering2008

    • Author(s)
      N. Honda, R. Potthast G. Nakamura, M. Sini
    • Journal Title

      Ann. Mat. Pure Appl. 87

      Pages: 7-37

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The geometric structure of a virtual turning point and the model of the Stokes geometry2008

    • Author(s)
      N. Honda
    • Journal Title

      RIMS Kokyuroku Bessatsu B10

      Pages: 63-113

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Principally tame regular sequences associated with the fourth Painleve hierarchy with a large parameter2008

    • Author(s)
      N. Honda, T. Aoki
    • Journal Title

      Proc. Japan Acad. 84

      Pages: 42-47

    • NAID

      40015931130

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Wavelet characterizations of weighted Herz spaces2008

    • Author(s)
      M. Izuki, K. Tachizawa
    • Journal Title

      Scientiae Mathematicae Japonicae 67

      Pages: 353-363

    • NAID

      10021089666

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ginzburg-Landau equations and solutions structure2008

    • Author(s)
      Shuichi JIMBO
    • Journal Title

      Sugaku Expositions, American Mathematical Society (in press)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The no-response approach and its relation to non-iterative methods for the inverse scattering2008

    • Author(s)
      Naofumi HONDA
    • Journal Title

      Ann. Mat. Pura Appl. 187

      Pages: 7-37

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Identification of a non-convex obstacle for acoustical scattering2007

    • Author(s)
      G. Nakamura, K. Yoshida
    • Journal Title

      J. Inverse III-Posed Probl 15

      Pages: 611-624

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A variational approach for an inverse dynamical problem for composite beams2007

    • Author(s)
      A. Morassi, G. Nakamura, K. Shirota, M. Sini
    • Journal Title

      European J. Appl. Math 18

      Pages: 21-55

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Identification of a non-convex obstacle for acoustical Scattering2007

    • Author(s)
      Gen NAKAMURA
    • Journal Title

      J. Inverse Ill-Posed Problem 15

      Pages: 611-624

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ginzburg-Landau equations and solution structure2007

    • Author(s)
      Shuichi JIMBO
    • Journal Title

      AMS Sugaku Translation (to appear)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Three spheres inequalities for a two-dimensional elliptic system and its application2007

    • Author(s)
      Gen Nakamura
    • Journal Title

      J. Differential Equations 232

      Pages: 329-351

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Unification of the probe and singular sources methods for the inverse boundary value problem by the no-response test2006

    • Author(s)
      G. Nakamura, R. Potthast, M. Sini
    • Journal Title

      Comm. Partial Differential Equations 31

      Pages: 1505-1528

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Unification of the probe and singular sources methods for the inverse boundary value problem by the no-response test2006

    • Author(s)
      Gen Nakamura
    • Journal Title

      Comm. Partial Differential Equations 31

      Pages: 1505-1528

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Entire solutions with merging fronts to reaction-diffusion equations2006

    • Author(s)
      Yoshihisa Morita
    • Journal Title

      J. Dynam. Differential Equations 18

      Pages: 841-861

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Phase pattern in a Ginzburg-Landau model with a discontinuous coefficient in a ring2006

    • Author(s)
      Yoshihisa Morita
    • Journal Title

      Discrete Contin. Dynam. Systems 14

      Pages: 149-168

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Ginzburg-Landau equations and solution structure2006

    • Author(s)
      Shuichi Jimbo
    • Journal Title

      Sugaku Expositions, American Mathematical Society 20(to appear)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Weighted L^p Sobolev - Lieb -Thirring inequalities2005

    • Author(s)
      K. Tachizawa
    • Journal Title

      Proc. of the Japan Acad 81

      Pages: 141-143

    • NAID

      120006459413

    • Related Report
      2008 Final Research Report
  • [Journal Article] Weighted Sobolev-Lieb -Thirring inequalities2005

    • Author(s)
      K. Tachizawa
    • Journal Title

      Rev. Mat. Iberoamericana 21

      Pages: 67-85

    • NAID

      120006456909

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] An inverse dynamical problem for connected beams2005

    • Author(s)
      Gen Nakamura
    • Journal Title

      European Journal Applied Mathematics 16

      Pages: 83-109

    • NAID

      120006459361

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Weighted Sobolev-Lieb-Thirring inequalities2005

    • Author(s)
      Kazuya Tachizawa
    • Journal Title

      Revista Mathematica Iberoamericana 21

      Pages: 67-85

    • NAID

      120006456909

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Recovery of residual stress in a vertically heterogeneous medium2005

    • Author(s)
      Gen Nakamura
    • Journal Title

      IMA Journal of Applied Mathematics 70

      Pages: 129-146

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Global bifurcation structure of one-dimensional Ginzburg-Landau model2005

    • Author(s)
      Yoshihisa Morita
    • Journal Title

      Journal of Mathematical Physics 46

      Pages: 1-24

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A variational approach to singular perturbation problems in reaction-diffusion systems2005

    • Author(s)
      Yoshihisa Morita
    • Journal Title

      Physica D 207

      Pages: 171-219

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Exponential decay phenomenon of the principal eigenvalue of an elliptic operator with a large drift term of gradient type

    • Author(s)
      S. Jimbo, M. Kimura, H. Notsu
    • Journal Title

      to appear in Asymptotic Analysis

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Wavelet characterization of weighted spaces

    • Author(s)
      K. Tachizawa
    • Journal Title

      to appear in RIMS Kokyuroku Bessatsu

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Wavelet characterization of weighted spaces

    • Author(s)
      K. Tachizawa
    • Journal Title

      RIMS Kokyuroku Bessatsu (to appear)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] 音響散乱逆問題における未知障害物の非解析境界点の同定2009

    • Author(s)
      中村玄
    • Organizer
      複素解析の発展とその応用
    • Place of Presentation
      群馬
    • Related Report
      2008 Final Research Report
  • [Presentation] Ginzburg-Landau equations and vortex motion2009

    • Author(s)
      Shuichi JIMBO
    • Organizer
      Analytic semigroups and related topicson the occasion of the centenary of The birth of Professor Kosaku Yosida
    • Place of Presentation
      University of Tokyo
    • Related Report
      2008 Annual Research Report
  • [Presentation] Spectra of domains with partial degeneration2008

    • Author(s)
      S. Jimbo
    • Organizer
      PDE seminar
    • Place of Presentation
      National Changhua Univ
    • Year and Date
      2008-12-19
    • Related Report
      2008 Final Research Report
  • [Presentation] Spectra of domains with partial degeneration2008

    • Author(s)
      S. Jimbo
    • Place of Presentation
      National Sun Yat-sen Univ
    • Year and Date
      2008-12-13
    • Related Report
      2008 Final Research Report
  • [Presentation] Eigenvalues of elliptic operators with variable coefficients in domains with small holes or thin tunnels2008

    • Author(s)
      S. Jimbo
    • Place of Presentation
      National Sun Yat-sen Univ
    • Year and Date
      2008-12-13
    • Related Report
      2008 Final Research Report
  • [Presentation] Spectral analysis of elliptic operators on a singularly perturbed domains2008

    • Author(s)
      S. Jimbo
    • Organizer
      PDE seminar
    • Place of Presentation
      Zhejiang University
    • Year and Date
      2008-11-07
    • Related Report
      2008 Final Research Report
  • [Presentation] Schatten- von Neumann classes of pseudodifferential operators2008

    • Author(s)
      K. Tachizawa
    • Organizer
      Harmonic Analysis and its Applications at Tokyo 2008
    • Place of Presentation
      首都大学東京
    • Year and Date
      2008-10-11
    • Related Report
      2008 Final Research Report
  • [Presentation] Schatten-von Neumann classes of pseudodifferential operators2008

    • Author(s)
      K. Tachizawa
    • Organizer
      Harmonic analysis and its Applications at Tokyo 2008
    • Place of Presentation
      首都大学東京
    • Year and Date
      2008-10-11
    • Related Report
      2008 Annual Research Report
  • [Presentation] Ginzburg-Landau equations and vortex motion2008

    • Author(s)
      Shuichi JIMBO
    • Organizer
      Analytic semigroups and related topics
    • Place of Presentation
      首都大学東京
    • Year and Date
      2008-10-11
    • Related Report
      2008 Annual Research Report
  • [Presentation] On the deformation of the Riemann manifold underlying a virtual turning point2008

    • Author(s)
      N. Honda
    • Organizer
      New approach to analytic equations, transformation theory, singular solutions and Stokes problem,
    • Place of Presentation
      RIMS, Kyoto University
    • Year and Date
      2008-09-17
    • Related Report
      2008 Annual Research Report
  • [Presentation] Spectral property of a singularly perturbed domain2008

    • Author(s)
      S. Jimbo
    • Organizer
      Perturbation of the resonant eigenvalues, Seoul Univ
    • Place of Presentation
      Hokkaido Univ, Joint seminar
    • Year and Date
      2008-01-25
    • Related Report
      2008 Final Research Report
  • [Presentation] Spectra of domains with partial degeneration-Perturbation of the resonant eigenvalues2008

    • Author(s)
      Shuichi JIMBO
    • Organizer
      Hokkaido University Seoul University joint seminar
    • Place of Presentation
      Seoul National University, Seoul
    • Year and Date
      2008-01-25
    • Related Report
      2007 Annual Research Report
  • [Presentation] The stratified Whitney jets and distribution of Gevrey classes and their idizations2008

    • Author(s)
      N. Honda
    • Organizer
      完全WKB解析と超局所解析
    • Place of Presentation
      京大数理研
    • Related Report
      2008 Final Research Report
  • [Presentation] The virtual turning points and the modelof the Stokes geometry2008

    • Author(s)
      N. Honda
    • Organizer
      Holomorphic PDEs, small divisors and summa bility
    • Place of Presentation
      CIRM
    • Related Report
      2008 Final Research Report
  • [Presentation] 非凸形状音響散乱体の同定2007

    • Author(s)
      中村玄
    • Organizer
      応用数理学会
    • Place of Presentation
      北海道大学
    • Year and Date
      2007-09-16
    • Related Report
      2008 Final Research Report
  • [Presentation] Spectra of domains with partial degeneration2007

    • Author(s)
      S. Jimbo
    • Organizer
      数学綜合報告会
    • Place of Presentation
      復旦大学
    • Year and Date
      2007-09-14
    • Related Report
      2008 Final Research Report
  • [Presentation] Wavelet characterization of weighted spaces2007

    • Author(s)
      K. Tachizawa
    • Organizer
      調和解析と非線形偏微分方程式
    • Place of Presentation
      京大数理研
    • Year and Date
      2007-07-10
    • Related Report
      2008 Final Research Report
  • [Presentation] Ginzburg-Landau equations in thin domains2007

    • Author(s)
      Shuichi JIMBO
    • Organizer
      Interntnl conference on Mathematical Theory of Superconductivity and Liquid Crystal
    • Place of Presentation
      East China Normal University, Shanghai
    • Year and Date
      2007-05-15
    • Related Report
      2007 Annual Research Report
  • [Presentation] The geometric structure of virtual turning points I, II2007

    • Author(s)
      N. Honda
    • Organizer
      Differential equations and exact WKB analysis
    • Place of Presentation
      RIMS
    • Related Report
      2008 Final Research Report
  • [Presentation] Ginzburg-Landau equations in thin domains2007

    • Author(s)
      S. Jimbo
    • Organizer
      International conference on mathematical theory of superconductivity and liquid crystal
    • Place of Presentation
      華東師範大学
    • Related Report
      2008 Final Research Report
  • [Presentation] マルチ領域をなす弾性体と固有振動2007

    • Author(s)
      神保秀一
    • Organizer
      非線型現象の数値シミュレーションと解析セミナー
    • Place of Presentation
      北大理学部
    • Related Report
      2008 Final Research Report
  • [Presentation] Spectra of domains with partial degeneration2007

    • Author(s)
      S. Jimbo
    • Organizer
      九州における偏微分方程式研究集会
    • Place of Presentation
      九大
    • Related Report
      2008 Final Research Report
  • [Presentation] Mathematical analysis for magnetic resonance Tomography2007

    • Author(s)
      G. Nakamura
    • Organizer
      九州における偏微分方程式研究集会
    • Place of Presentation
      九大
    • Related Report
      2008 Final Research Report
  • [Presentation] Ginzburg-Landau equation and vortex motion2006

    • Author(s)
      S. Jimbo
    • Organizer
      Analytic semigroups and related topics, on the occasion of the centenary of the birth of Professor Kosaku Yosida
    • Place of Presentation
      Univ. Tokyo
    • Related Report
      2008 Final Research Report
  • [Presentation] ストークス幾何の実線破線決定条件について2006

    • Author(s)
      本多尚文
    • Organizer
      微分方程式系の代数解析と完全WKB 解析
    • Place of Presentation
      京大数理解析研
    • Related Report
      2008 Final Research Report
  • [Presentation] Ginzburg-Landau equations in thin domains2006

    • Author(s)
      S. Jimbo
    • Organizer
      散逸系におけるパターン形成問題
    • Place of Presentation
      RIMS
    • Related Report
      2008 Final Research Report
  • [Presentation] Ginzburg-Landau equations inthin domains2006

    • Author(s)
      S. Jimbo
    • Organizer
      Workshop on singularities in PDE and the calculus of variations
    • Place of Presentation
      Centre de Recherches Mathematiques Univ. of Montreal
    • Related Report
      2008 Final Research Report
  • [Presentation] On the Stokes geometry of NoumiYamada systems2006

    • Author(s)
      N.Honda
    • Organizer
      Algebraic analytic and geometric aspects of complex differential equations and their deformation of Painleve Hierarchies
    • Place of Presentation
      RIMS
    • Related Report
      2008 Final Research Report
  • [Presentation] The uncertainty principle, wavelets, eigenvalues of the Schro dinger operator2006

    • Author(s)
      K.Tachizawa
    • Organizer
      第7回北東数学解析研究会
    • Place of Presentation
      北大
    • Related Report
      2008 Final Research Report
  • [Presentation] A generalization of the Sobolev-Lieb-Thirring inequality2005

    • Author(s)
      K. Tachizawa
    • Organizer
      SNU-HU 3rd Joint Symposium on Mathematics
    • Place of Presentation
      Seoul Univ.
    • Year and Date
      2005-10-14
    • Related Report
      2008 Final Research Report
  • [Presentation] 領域の退化と固有値の漸近挙動2005

    • Author(s)
      神保秀一
    • Organizer
      日本数学会, 応用数学分科会特別講演
    • Place of Presentation
      岡山大学
    • Year and Date
      2005-09-21
    • Related Report
      2008 Final Research Report
  • [Presentation] Weighted L^p Sobolev-Lieb-Thirring inequalities2005

    • Author(s)
      立澤一哉
    • Organizer
      日本数学会, 実函数論分科会
    • Place of Presentation
      岡山大学
    • Year and Date
      2005-09-21
    • Related Report
      2008 Final Research Report
  • [Presentation] Greedy bases in weighted spaces2005

    • Author(s)
      立澤一哉
    • Organizer
      日本数学会, 実函数論分科会
    • Place of Presentation
      岡山大学
    • Year and Date
      2005-09-21
    • Related Report
      2008 Final Research Report
  • [Presentation] An application of Frazier -Jawerth's phi-transform to the Sobolev -Lieb-Thirring inequalities2005

    • Author(s)
      K. Tachizawa
    • Organizer
      the Special Semester "Modern Methods of Time -Frequency Analysis" SPRING 2005
    • Place of Presentation
      at the Erwin Schrodinger Institute
    • Year and Date
      2005-06-10
    • Related Report
      2008 Final Research Report
  • [Presentation] Singular deformation of domains and spectral asymptotics2005

    • Author(s)
      S. Jimbo
    • Organizer
      6th AIMS international conferences Univ.
    • Place of Presentation
      Poitier
    • Related Report
      2008 Final Research Report
  • [Presentation] Singular deformation of domains and spectral analysis2005

    • Author(s)
      S. Jimbo
    • Organizer
      Hokkaido Univ. Seoul Univ. Joint seminar
    • Place of Presentation
      Seoul Univ.
    • Related Report
      2008 Final Research Report
  • [Presentation] A unified method for identifying the discontinuity of a medium2005

    • Author(s)
      G.Nakamura
    • Organizer
      Inverse problems, multiscale analysis and homogenization
    • Place of Presentation
      Seoul National Univ
    • Related Report
      2008 Final Research Report
  • [Book] ギンツブルクーランダウ方程式と安定性解析2009

    • Author(s)
      神保秀一, 森田善久
    • Total Pages
      335
    • Publisher
      岩波数学叢書, 岩波書店
    • Related Report
      2008 Final Research Report
  • [Book] ギンツブルクーランダウ方程式と安定性解析2009

    • Author(s)
      神保秀一, 森田善久
    • Total Pages
      335
    • Publisher
      岩波書店
    • Related Report
      2008 Annual Research Report
  • [Book] 偏微分方程式入門2006

    • Author(s)
      神保秀一
    • Total Pages
      223
    • Publisher
      共立出版
    • Related Report
      2008 Final Research Report
  • [Book] 偏微分方程式入門2006

    • Author(s)
      神保 秀一
    • Total Pages
      221
    • Publisher
      共立出版
    • Related Report
      2006 Annual Research Report

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Published: 2005-04-01   Modified: 2016-04-21  

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