Geometric analysis of dispersive flow

2011 Fiscal Year Final Research Report

• Project/Area Number: 21740101
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Kochi University (2011); Kyushu University (2009-2010)
• Principal Investigator: ONODERA Eiji 高知大学, 教育研究部・自然科学系, 准教授 (70532357)
• Project Period (FY): 2009 – 2011
• Keywords: 分散型偏微分方程式 / 初期値問題 / 幾何解析

Research Abstract

The initial value problem for a third order nonlinear dispersive curve flow on compact almost hermitian manifolds was mainly investigated. The relationship between the unique solvability of the initial value problem and the geometric setting was studied. Some methods of solving one-dimensional dispersive equations for complex valued functions and geometric analysis of nonlinear partial differential equations were applied to solve the initial value problem.

Research Products

• [Journal Article] A Curve Flow on an Almost Hermitian Manifold Evolved by a Third Order Dispersive Equation (2012)
  • Author(s): Eiji Onodera
  • Journal Title: FUNKCIALAJ EKVACIOJ Volume: 55 Pages: 137-156
  • Peer Reviewed
• [Journal Article] A remark on the global existence of a third order dispersive flow into locally Hermitian symmetric spaces (2010)
  • Author(s): Eiji Onodera
  • Journal Title: Communications in Partial Differential Equations Volume: 35 Pages: 1130-1144
  • Peer Reviewed
• [Journal Article] A third order dispersive flow for closed curves into almost Hermitian manifolds (2009)
  • Author(s): Hiroyuki Chihara and Eiji Onodera
  • Journal Title: Journal of Functional Analysis Volume: 257 Pages: 388-404
  • Peer Reviewed
• [Presentation] A third order dispersive flow into compact almost Hermitian manifolds (2011)
  • Author(s): 小野寺栄治
  • Organizer: Linear and Nonlinear Waves No.9
  • Place of Presentation: ピアザ淡海滋賀県立県民交流センター
  • Year and Date: 2011-11-04
• [Presentation] A third order dispersive flow into almost Hermitian manifolds (2011)
  • Author(s): 小野寺栄治
  • Organizer: 非線形解析セミナー
  • Place of Presentation: 慶応大学
  • Year and Date: 2011-07-01
• [Presentation] A third order dispersive flow into almost Hermitian manifolds (2011)
  • Author(s): 小野寺栄治
  • Organizer: 若手のための偏微分方程式と数学解析
  • Place of Presentation: 九州大学
  • Year and Date: 2011-02-17
• [Presentation] A third order dispersive flow into almost Hermitian manifolds (2010)
  • Author(s): 小野寺栄治
  • Organizer: 数理科学セミナー
  • Place of Presentation: 茨城大学
  • Year and Date: 2010-03-22
• [Presentation] A third order dispersive flow into almost Hermitian manifolds (2009)
  • Author(s): 小野寺栄治
  • Organizer: 研究集会「微分方程式の総合的研究」
  • Place of Presentation: 東京大学
  • Year and Date: 2009-12-19
• [Presentation] The initial value problem for a third order dispersive flow into compact almost Hermitian manifolds (2009)
  • Author(s): 小野寺栄治
  • Organizer: NLPDEセミナー
  • Place of Presentation: 京都大学
  • Year and Date: 2009-07-10
• [Presentation] The initial value problem for a third-order dispersive flow into compact almost Hermitian manifolds (2009)
  • Author(s): 小野寺栄治
  • Organizer: 名古屋微分方程式セミナー
  • Place of Presentation: 名古屋大学
  • Year and Date: 2009-06-15
• [Presentation] A third-order dispersive flow into compact almost Hermitian manifolds (2009)
  • Author(s): 小野寺栄治
  • Organizer: RIMS共同研究「非線形双曲型および分散型方程式の解の挙動について」
  • Place of Presentation: 京都大学
  • Year and Date: 2009-05-26
• [Presentation] The initial value problem for a third-order dispersive flow into compact almost Hermitian manifolds (2009)
  • Author(s): 小野寺栄治
  • Organizer: 微分方程式セミナー
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-05-15
• [Remarks]
  • URL: http://www.math.kochi-u.ac.jp/onodera/