Asymptotic properties of solutions to nonlinear dispersive partial differential equations

2011 Fiscal Year Final Research Report

• Project/Area Number: 21740102
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: The University of Tokyo (2011); Tokyo Metropolitan University (2009-2010)
• Principal Investigator: SHIMOMURA Akihiro 東京大学, 大学院・数理科学研究科, 准教授 (00365066)
• Project Period (FY): 2009 – 2011
• Keywords: 解析学 / 偏微分方程式 / 関数解析

Research Abstract

I studied the large time behavior of solutions to the Schrodinger equation with long-range nonlinear dissipation, the time decay estimate of solutions to the Hartree-Fock type equation with a long-range potential and the large time behavior of solutions to the Dirac-Klein-Gordon system in two space dimensions.

Research Products

• [Journal Article] Dispersive global solutions to thetime-dependent Hartree-Fock typeequation with a long-range potential (2009)
  • Author(s): Akihiro Shimomura
  • Journal Title: Journal of Mathematical Sciences, The University of Tokyo Volume: 16巻 Pages: 239-267
  • Peer Reviewed
• [Journal Article] Large time behavior of solutions to Schrodinger equations with a dissipative nonlinearity for arbitrarily large initial data (2009)
  • Author(s): Naoyasu Kita and Akihiro Shimomura
  • Journal Title: Journal of the Mathematical Society of Japan Volume: 61巻 Pages: 39-64
  • Peer Reviewed
• [Journal Article] A remark on the algebraic normal form method applied to the Dirac-Klein-Gordon system in two space dimensions
  • Author(s): Masahiro Ikeda, Akihiro Shimomuraand Hideaki Sunagawa
  • Journal Title: 数理解析研究所講究録別冊 Volume: (掲載確定)
  • Peer Reviewed
• [Presentation] 非線型分散型発展方程式について (2011)
  • Author(s): 下村明洋
  • Organizer: 数理科学講演会
  • Place of Presentation: 東京大学
  • Year and Date: 2011-11-25
• [Presentation] シュワルツ超関数とその周辺 (2010)
  • Author(s): 下村明洋
  • Organizer: 第四回数理情報科学コロキウム@秋葉原
  • Place of Presentation: 首都大学東京(秋葉原サテライトキャンパス)
  • Year and Date: 2010-05-29
• [Presentation] 非線型消散項を伴うシュレディンガー方程式の任意の大きさの初期データに対する解の漸近挙動(北直泰氏との共同研究) (2009)
  • Author(s): 下村明洋
  • Organizer: スペクトル理論セミナー
  • Place of Presentation: 学習院大学
  • Year and Date: 2009-12-12
• [Presentation] Large time behavior of solutions toSchrodinger equations with nonlineardissipation for arbitrarily large initialdata(北直泰氏との共同研究) (2009)
  • Author(s): Akihiro Shimomura
  • Organizer: 研究集会「非線形分散型方程式・波動方程式の初期値問題の適切性と散乱理論」
  • Place of Presentation: 北海道大学
  • Year and Date: 2009-11-23
• [Presentation] 長距離型ポテンシャルを伴うHartree-Fock方程式の解の分散性について (2009)
  • Author(s): 下村明洋
  • Organizer: 微分方程式セミナー
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-06-26
• [Presentation] 「非線型消散項を伴うシュレディンガー方程式の任意の大きさの初期データに対する解の漸近挙動」(北直泰氏との共同研究) (2009)
  • Author(s): 下村明洋
  • Organizer: 神楽坂解析セミナー
  • Place of Presentation: 東京理科大学
  • Year and Date: 2009-05-23
• [Presentation] 「非線型消散項を伴うシュレディンガー方程式の任意の大きさの初期データに対する解の漸近挙動」(北直泰氏との共同研究) (2009)
  • Author(s): 下村明洋
  • Organizer: 解析学火曜セミナー
  • Place of Presentation: 東京大学
  • Year and Date: 2009-04-28