Asymptotic behavior of solutions to nonlinear dispersive equations

• Project/Area Number: 19840036
• Research Category: Grant-in-Aid for Young Scientists (Start-up)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: Fukuoka University of Education
• Principal Investigator: SEGATA Jun-ichi Fukuoka University of Education, 教育学部, 准教授 (90432822)
• Project Period (FY): 2007 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥2,304,000 (Direct Cost: ¥1,980,000、Indirect Cost: ¥324,000); Fiscal Year 2008: ¥1,404,000 (Direct Cost: ¥1,080,000、Indirect Cost: ¥324,000); Fiscal Year 2007: ¥900,000 (Direct Cost: ¥900,000)
• Keywords: 関数方程式論 / 数理物理学 / 漸近解析 / 調和解析 / 流体 / 数理物理

Research Abstract

本研究では流体中の渦糸運動といった, 物理学, 工学に現れる非線形偏微分方程式の解の振る舞いを調べることを通して, 流体運動の数学的理論の構築を試みた. 具体的には, 軸対称な渦糸の運動を近似する非線形偏微分方程式の解の長時間挙動をフーリエ解析といった数学の手法を用いて解析した. 更にこの方程式よりも, より渦糸の運動を高次近似している非線形偏微分方程式の解の長時間挙動についても調べた. この方程式は非線形性が強いため解析が難しいが, 本研究では特殊解の構成, 線形化方程式の解析により解の挙動についてのいくつかの見通しを与えることができた.

Research Products

• [Journal Article] On asymptotic behavior of solutions to Korteweg-de Vries type equations related to vortex filament with axial flow (2008)
  • Author(s): Segata Jun-ichi
  • Journal Title: Journal of Differential Equations Vol.245, No.2 Pages: 281-306
  • Peer Reviewed
• [Journal Article] On asymptotic behavior of solutions to Korteweg-de Vries type equations related to vortex filament with axial flow (2008)
  • Author(s): Jun-ichi Segata
  • Journal Title: Journal of Differential Equations 245 Pages: 281-306
  • Peer Reviewed
• [Journal Article] On asymptotic behavior of solutions to the fourth order cubic nonlinear Schrodinger type equation (2007)
  • Author(s): Segata Jun-ichi
  • Journal Title: Asmptotic Analysis and singularities -hyperbolic and dispersive PDEs and fluid mechanics, Advanced Studies Pure Mathematics Vol.47, No.1 Pages: 329-339
  • Peer Reviewed
• [Journal Article] Shimomura Akihiro, Global existence and asymptotic behavior of solutions to the fourth order nonlinear Schrodinger type equation (2007)
  • Author(s): Segata Jun-ichi
  • Journal Title: Communications in Applied Analysis Vol.11. No.2 Pages: 169-188
  • Peer Reviewed
• [Journal Article] Global existence and asymptotic behavior of solutions to the fourth order nonlinear Schrodinger type equation (2007)
  • Author(s): Jun-ichi Segata
  • Journal Title: Communications in Applied Analysis 11 Pages: 169-188
  • Peer Reviewed
• [Journal Article] On asymptotic behavior of solutions to the fourth order cubic nonlinear Schrodinger type equation (2007)
  • Author(s): Jun-ichi Segata
  • Journal Title: Advanced Studies in Pure Mathematics 47 Pages: 329-339
  • Peer Reviewed
• [Remarks] Segata Jun-ichi, Final state problem for some KdV type equation. 京都大学数理解析研究所研究集会調和解析学と非線形偏微分方程式 (Workshop on Harmonic Analysis and NonlinearPartial Differential Equations). 2007年7/9-7/11京都大学数理解析研究所京都市.
• [Remarks] 瀬片純市,非線形Schrodinger 方程式の長距離散乱理論について.スプリングスクール 2008 サーベイレクチャーシリーズ ~非線形の数学解析~.2008年2/14-2/16東北大学 仙台市.
• [Remarks] Segata Jun-ichi, On higher order nonlinear Schrodinger type equation. National Chiao Tung University conference. 2008年3/18 National Chiao Tung University, Hsinchu, Taiwan.
• [Remarks] Segata Jun-ichi, On higher order nonlinear Schrodinger type equation. Academia Sinica Analysis Seminar. 2008年 3/24 Academia Sinica, Taipei, Taiwan.