High frequency asymptotic analysis for nonlinear partial differential equations

• Project/Area Number: 25400161
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Osaka University
• Principal Investigator: Sunagawa Hideaki 大阪大学, 理学研究科, 准教授 (80375394)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 高周波漸近解析 / 非線形 / 双曲型方程式 / 分散型方程式 / シュレディンガー方程式 / 零構造 / ライフスパン / 非線形消散構造 / 波動方程式 / 非線形消散 / 非線形シュレディンガー方程式 / 漸近解析

Outline of Final Research Achievements

Nonlinear partial differential equations of hyperbolic and dispersive type have been studied from the viewpoint of high frequency asymptotic analysis. A sharp lower bound estimate for the lifespan of small data solutions to nonlinear Schrodinger equations has been provided. Several results have been obtained concerning resonance-type behavior, null structure and dissipative structure for nonlinear Schrodinger systems with multiple masses.

Research Products

• [Int'l Joint Research] 延辺大学(中国)
• [Int'l Joint Research] 延辺大学(中国)
• [Journal Article] Remarks on derivative nonlinear Schodinger systems with multiple masses (2017)
  • Author(s): Chunhua Li, Hideaki Sunagawa
  • Journal Title: Proceedings of the conference "Asymptotic Analysis for Nonlinear Dispersive and Wave Equations" Volume: 未定
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] On Schrodinger systems with cubic dissipative nonlinearities of derivative type (2016)
  • Author(s): Chunhua Li, Hideaki Sunagawa
  • Journal Title: Nonlinearity Volume: 29 Issue: 5 Pages: 1537-1563
  • DOI: 10.1088/0951-7715/29/5/1537
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] The lifespan of small solutions to cubic derivative nonlinear Schrodinger equations in one space dimension (2016)
  • Author(s): Yuji Sagawa, Hideaki Sunagawa
  • Journal Title: Discrete and Continuous Dynamical Systems Ser.A Volume: 未定
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Semilinear hyperbolic systems violating the null condition (2015)
  • Author(s): Soichiro Katayama, Toshiaki Matoba and Hideaki Sunagawa
  • Journal Title: Mathematische Annalen Volume: 361 (1-2) Issue: 1-2 Pages: 275-312
  • DOI: 10.1007/s00208-014-1071-1
  • Peer Reviewed
• [Journal Article] Energy decay for systems of semilinear wave equations with dissipative structure in two space dimensions (2015)
  • Author(s): Soichiro Katayama, Akitaka Matsumura, Hideaki Sunagawa
  • Journal Title: Nonlinear Differential Equations and Applications NoDEA Volume: 未定 Issue: 4 Pages: 601-628
  • DOI: 10.1007/s00030-014-0297-7
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] A remark on decay rates of solutions for a system of quadratic nonlinear Schrodinger equations in 2D (2014)
  • Author(s): Soichiro Katayama, Chunhua Li, Hideaki Sunagawa
  • Journal Title: Differential and Integral Equations Volume: 27 Pages: 301-312
  • Peer Reviewed
• [Journal Article] Remarks on decay of small solutions to systems of Klein-Gordon equations with dissipative nonlinearities (2014)
  • Author(s): Donghyun Kim, Hideaki Sunagawa
  • Journal Title: Nonlinear Analysis: Theory, Methods & Applications Volume: 97 Pages: 94-105
  • DOI: 10.1016/j.na.2013.11.025
  • Peer Reviewed
• [Journal Article] Null structure in a system of quadratic derivative Schroedinger equations (2014)
  • Author(s): Masahiro Ikeda, Soichiro Katayama and Hideaki Sunagawa
  • Journal Title: Annales Henri Poincare Volume: 印刷中(電子出版済) Issue: 2 Pages: 535-567
  • DOI: 10.1007/s00023-014-0316-6
  • Peer Reviewed
• [Presentation] Remarks on derivative nonlinear Schrodinger systems with multiple masses (2017)
  • Author(s): Chunhua Li, Hideaki Sunagawa
  • Organizer: 日本数学会2016年度年会
  • Place of Presentation: 首都大学東京
  • Year and Date: 2017-03-27
• [Presentation] The lifespan of small solutions to cubic derivative nonlinear Schrodinger equations in one space dimension (2016)
  • Author(s): Hideaki Sunagawa
  • Organizer: Nonlinear Wave and Dispersive Equations, Kyoto 2016
  • Place of Presentation: 京都大学
  • Year and Date: 2016-09-06
  • Int'l Joint Research / Invited
• [Presentation] The lifespan of small solutions to cubic derivative nonlinear Schrodinger equations in one space dimension (2016)
  • Author(s): 佐川 侑司、砂川 秀明
  • Organizer: 日本数学会2016年度年会
  • Place of Presentation: 筑波大学（茨城県つくば市）
  • Year and Date: 2016-03-19
• [Presentation] 微分型の非線形消散項を伴うシュレディンガー方程式系について (2015)
  • Author(s): 砂川 秀明、Chunhua Li
  • Organizer: 日本数学会2015年度秋季総合分科会
  • Place of Presentation: 京都産業大学（京都市左京区）
  • Year and Date: 2015-09-15
• [Presentation] On Schrodinger systems with cubic dissipative nonlinearities of derivative type (2015)
  • Author(s): Hideaki Sunagawa
  • Organizer: Workshop on partial differential equations and numerical analysis
  • Place of Presentation: 延辺大学（中国、延吉）
  • Year and Date: 2015-07-07
  • Int'l Joint Research / Invited
• [Presentation] Agemi-type structural condition for systems of nonlinear wave equations (2015)
  • Author(s): Hideaki Sunagawa
  • Organizer: 第32回九州における偏微分方程式研究集会
  • Place of Presentation: 九州大学西新プラザ （福岡市早良区）
  • Year and Date: 2015-01-30
  • Invited
• [Presentation] Null structure in derivative nonlinear Schrodinger systems (2014)
  • Author(s): Hideaki Sunagawa
  • Organizer: 1st Partial Differential Equations Seminar in Yanbian University
  • Place of Presentation: 延辺大学 （中国、延吉市）
  • Year and Date: 2014-09-17
  • Invited
• [Presentation] Null structure in a system of quadratic derivative nonlinear Schrodinger equations
  • Author(s): Hideaki Sunagawa
  • Organizer: Mexico-Japan joint meeting on PDE at Morelia
  • Place of Presentation: メキシコ国立自治大学
  • Invited
• [Presentation] Null structure in a system of quadratic derivative nonlinear Schrodinger equations
  • Author(s): Hideaki Sunagawa
  • Organizer: 第3回弘前非線形方程式研究会
  • Place of Presentation: 弘前大学
  • Invited
• [Funded Workshop] The 14th Linear and Nonlinear Waves (2016)
  • Place of Presentation: ピアザ淡海 滋賀県立国際交流センター（滋賀県大津市）
  • Year and Date: 2016-11-02
• [Funded Workshop] The 13th Linear and Nonlinear Waves (2015)
  • Place of Presentation: ピアザ淡海 滋賀県立県民交流センター（滋賀県大津市）
  • Year and Date: 2015-11-03