Null structure and high frequency asymptotic analysis for nonlinear hyperbolic and dispersive equations

• Project/Area Number: 17K05322
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Osaka City University (2020-2021); Osaka University (2017-2019)
• Principal Investigator: Sunagawa Hideaki 大阪市立大学, 大学院理学研究科, 教授 (80375394)
• Project Period (FY): 2017-04-01 – 2022-03-31
• Project Status: Completed (Fiscal Year 2021)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 零構造 / 弱消散構造 / 非線形シュレディンガー方程式 / 非線形波動方程式 / 微分型非線形シュレディンガー方程式 / 弱い消散構造 / 弱零構造 / 高周波漸近解析 / 双曲型方程式 / 分散型方程式 / 非線形

Outline of Final Research Achievements

Null structure and the related properties for nonlinear partial differential differential equations of hyperbolic and dispersive type have been studied from the view point of high frequency asymptotic analysis. In particular, weakly dissipative structure has been revealed for semilinear wave equations and derivative nonlinear Schrodinger equations. Several results have been obtained concerning decay properties of solutions to these equations.

Academic Significance and Societal Importance of the Research Achievements

非線形シュレディンガー方程式における弱消散構造は、例えば光学に現れる諸問題と密接な関わりがあるため、それを解明することは幅広い応用につながる可能性を秘めていると期待される。また、線形偏微分方程式に対する高周波漸近解析の研究が超局所解析やフーリエ積分作用素の理論を誕生させ発展させたことを思い出すならば、それらの非線形版に相当する手法を整備して一つの理論体系に昇華させる試みは、純粋数学としても意義があると考えられる。

Research Products

• [Int'l Joint Research] 延辺大学(中国)
• [Int'l Joint Research] 延辺大学(中国)
• [Int'l Joint Research] 延辺大学(中国)
• [Int'l Joint Research] 延辺大学(中国)
• [Journal Article] On the derivative nonlinear Schrodinger equation with weakly dissipative structure (2021)
  • Author(s): Chunhua Li, Yoshinori Nishii, Yuji Sagawa, Hideaki Sunagawa
  • Journal Title: Journal of Evolution Equations Volume: - Issue: 2 Pages: 1541-1550
  • DOI: 10.1007/s00028-020-00634-6
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Energy decay for small solutions to semilinear wave equations with weakly dissipative structure (2021)
  • Author(s): Yoshinori Nishii, Hideaki Sunagawa, Hiroki Terashita
  • Journal Title: Journal of the Mathematical Society of Japan Volume: 73 Issue: 3 Pages: 767-779
  • DOI: 10.2969/jmsj/84148414
  • NAID: 130008067986
  • ISSN: 0025-5645, 1881-1167, 1881-2333
  • Peer Reviewed
• [Journal Article] Large time asymptotics for a cubic nonlinear Schrodinger system in one space dimension, II (2021)
  • Author(s): Chunhua Li, Yoshinori Nishii, Yuji Sagawa, Hideaki Sunagawa
  • Journal Title: Tokyo Journal of Mathematics Volume: - Issue: 2
  • DOI: 10.3836/tjm/1502179340
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] On Agemi-type structural conditions for a system of semilinear wave equations (2020)
  • Author(s): Yoshinori Nishii, Hideaki Sunagawa
  • Journal Title: Journal of Hyperbolic Differential Equations Volume: 17 Issue: 03 Pages: 459-473
  • DOI: 10.1142/s0219891620500125
  • Peer Reviewed
• [Journal Article] Small data global existence for a class of quadratic derivative nonlinear Schrodinger systems in two space dimensions (2020)
  • Author(s): Sakoda Daisuke、Sunagawa Hideaki
  • Journal Title: Journal of Differential Equations Volume: 268 Issue: 4 Pages: 1722-1749
  • DOI: 10.1016/j.jde.2019.09.032
  • Peer Reviewed
• [Journal Article] Large time asymptotics for a cubic nonlinear Schrodinger system in one space dimension (2020)
  • Author(s): C.Li, Y.Nishii, Y.Sagawa, H.Sunagawa
  • Journal Title: Funkcialaj Ekvacioj Volume: -
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] A sharp lower bound for the lifespan of small solutions to the Schrodinger equation with a subcritical power nonlinearity (2018)
  • Author(s): Yuji Sagawa, Hideaki Sunagawa, Shunsuke Yasuda
  • Journal Title: Differential and Integral Equations Volume: ー
  • Peer Reviewed
• [Presentation] On the derivative nonlinear Schrodinger equation with weakly dissipative structure (2021)
  • Author(s): Chunhua Li, 西井良徳、佐川侑司、砂川秀明
  • Organizer: 日本数学会2021年度秋季総合分科会
• [Presentation] Energy decay for small solutions to semilinear wave equations with weakly dissipative structure (2020)
  • Author(s): 西井良徳、砂川秀明、寺下拓貴
  • Organizer: 日本数学会2020年度秋季総合分科会
• [Presentation] Large time asymptotics for a cubic nonlinear Schrodinger system in one space dimension, II (2020)
  • Author(s): Chunhua Li、西井良徳、佐川侑司、砂川秀明
  • Organizer: 日本数学会2020年度秋季総合分科会
• [Presentation] Large time asymptotics for a cubic nonlinear Schrodinger system in one space dimension (2020)
  • Author(s): Chunhua Li 西井 良徳、佐川 侑司、砂川 秀明
  • Organizer: 日本数学会2020年度年会
• [Presentation] 半線形波動方程式系に対するAgemi型の構造条件について (2019)
  • Author(s): 西井 良徳、砂川 秀明
  • Organizer: 日本数学会2019年度秋季総合分科会
• [Presentation] Small data global existence for a class of quadratic derivative nonlinear Schrodinger systems in two space dimensions (2018)
  • Author(s): Hideaki Sunagawa
  • Organizer: RIMS workshop "Harmonic analysis and nonlinear partial differential equations"
  • Int'l Joint Research / Invited
• [Presentation] Small data global existence for a class of quadratic derivative nonlinear Schrodinger systems in two space dimensions (2018)
  • Author(s): Hideaki Sunagawa
  • Organizer: Seminar on PDE with Dissipative Structure 2018
  • Int'l Joint Research / Invited
• [Presentation] Small data global existence for a quadratic derivative nonlinear Schrodinger system in two space dimensions (2018)
  • Author(s): 迫田大輔、砂川秀明
  • Organizer: 日本数学会2018年度年会
• [Presentation] On derivative nonlinear Schrodinger systems with multiple masses (2017)
  • Author(s): Hideaki Sunagawa
  • Organizer: RIMS workshop "Nonlinear Wave and Dispersive Equations"
  • Int'l Joint Research / Invited
• [Presentation] A sharp lower bound for the lifespan of small solutions to the Schrodinger equation with a subcritical power nonlinearity (2017)
  • Author(s): 佐川侑司、砂川秀明、保田舜介
  • Organizer: 日本数学会2017年度秋季総合分科会
• [Funded Workshop] The 17th Linear and Nonlinear Waves (2019)
• [Funded Workshop] The 15th Linear and Nonlinear Waves (2017)