Long time behavior and singular limit for solution tononlinear dispersive equation

• Project/Area Number: 21740122
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: Tohoku University (2010-2012); Fukuoka University of Education (2009)
• Principal Investigator: SEGATA Jun-ichi 東北大学, 大学院・理学研究科, 准教授 (90432822)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000); Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: 非線形現象 / 関数方程式論 / 数理物理学 / 漸近解析 / 調和解析学 / 流体 / 漸近挙動 / 調和解析 / 数理理物理学

Research Abstract

We considered the long time behavior of solutions to nonlinear dispersive partial differential equations arises in various fields of physics and engineering. Especially, we focused on solvability, scattering problem, and the stability of some special solutions called standing waves for the higher order nonlinear Schrodinger type equation arising in context of the motion of vortex filament. We also studied the semiclassical limit of Schrodinger-KdV system which describes an interaction betweenlong and short waves.

Research Products

• [Journal Article] Refined energy inequality with application to well-posedness for the fourth order nonlinear Schrodinger type equation on torus (2012)
  • Author(s): Jun-ichi Segata
  • Journal Title: Journal of Differential Equations Volume: Vol. 252 Issue: 11 Pages: 5994-6011
  • DOI: 10.1016/j.jde.2012.02.016
  • Peer Reviewed
• [Journal Article] Well-posedness and standing waves for the fourth-order non-linear Schrodinger-type equation (2011)
  • Author(s): Jun-ichi Segata
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: Vol.B26 Pages: 81-92
  • Peer Reviewed
• [Journal Article] The initial value problem for some hyperbolic-dispersive system (2011)
  • Author(s): Shuichi Kawashima, Chi-Kun Lin, and Jun-ichi Segata
  • Journal Title: Mathematical Methods in Applied Sciences Volume: Vol.35 Issue: 2 Pages: 125-133
  • DOI: 10.1002/mma.1542
  • Peer Reviewed
• [Journal Article] A remark on asymptotics of solutions to Schrodinger equation with fourth order dispersion (2011)
  • Author(s): Jun-ichi Segata
  • Journal Title: Asymptotic Analysis Volume: 75 Issue: 1-2 Pages: 25-36
  • DOI: 10.3233/asy-2011-1051
  • Peer Reviewed
• [Journal Article] Existence and Stability of Standing Waves of Fourth Order Nonlinear Schrödinger Type Equation Related to Vortex Filament (2011)
  • Author(s): Masaya Maeda and Jun-ichi Segata
  • Journal Title: Funkcialaj Ekvacioj Volume: 54 Issue: 1 Pages: 1-14
  • DOI: 10.1619/fesi.54.1
  • NAID: 130000654777
  • ISSN: 0532-8721
  • Peer Reviewed
• [Journal Article] Well-posedness and existence of standing waves for the fourth order nonlinear Schrodinger type equation (2010)
  • Author(s): Jun-ichi Segata
  • Journal Title: Discrete and Continuous Dynamical Systems.Series Volume: Vol.27 Issue: 3 Pages: 1093-1105
  • DOI: 10.3934/dcds.2010.27.1093
  • Peer Reviewed
• [Journal Article] Final state problem for some KdV type equation (2010)
  • Author(s): Jun-ichi Segata
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: Vol.B22 Pages: 13-20
  • Peer Reviewed
• [Journal Article] Well-posedness and existence of standing waves for the fourth order nonlinear Schrodinger type equation (2010)
  • Author(s): Jun-ichi Segata
  • Journal Title: Discrete and Continuous Dynamical Systems. Series A Volume: Vol.27 Pages: 1093-1105
  • Peer Reviewed
• [Presentation] KdV, nonlinear Schrodinger equations-I , KdV, nonlinear Schrodinger equations-II" NCTS/CMMSC Seminar on PDEs (2012)
  • Author(s): Jun-ichi Segata
  • Organizer: Theory and Applications
  • Place of Presentation: National Chiao Tung University, Hsinchu, Taiwan.
  • Year and Date: 2012-10-31
• [Presentation] Well-posedness for the fourth order nonlinear Schrodinger type equation on torus (2012)
  • Author(s): 瀬片純市
  • Organizer: 日本数学会2012年度秋季総合分科会
  • Place of Presentation: 九州大学 福岡市
  • Year and Date: 2012-09-21
• [Presentation] Well-posedness for the fourth order nonlinear Schrodinger type equation on torus (2012)
  • Author(s): 瀬片純市
  • Organizer: 日本数学会2012年度秋季総合分科会
  • Place of Presentation: 九州大学(福岡市)
• [Presentation] Long time behavior of solutions to non-linear Schrodinger equations with higher order dispersion (2011)
  • Author(s): Jun-ichi Segata
  • Organizer: The 4th MSJ-SI"Nonlinear Dynamics in Partial Differential Equations"
  • Place of Presentation: 九州大学 福岡市
  • Year and Date: 2011-09-21
• [Presentation] Long time behavior of solutions to non-linear Schrodinger equations with higher order dispersion (2011)
  • Author(s): Jun-ichi Segata
  • Organizer: The 4^<th> MSJ-SI "Nonlinear Dynamics in Partial Differential Equations"
  • Place of Presentation: 九州大学
  • Year and Date: 2011-09-21
• [Presentation] Well-posedness and standing waves for the fourth-ordernon-linear Schrodinger-type equation (2010)
  • Author(s): Jun-ichi Segata
  • Organizer: Workshop on Harmonic Analysis and Nonlinear Partial Differential Equations
  • Place of Presentation: 京都大学数理解析研究所 京都市
  • Year and Date: 2010-07-07
• [Presentation] 高階非線形分散型方程式の 解の長時間挙動 (2010)
  • Author(s): 瀬片純市
  • Organizer: 日本数学会2010年度年会(特別講演)
  • Place of Presentation: 慶応義塾大学 横浜市
  • Year and Date: 2010-03-27
• [Presentation] 高階非線形分散型方程式の解の長時間挙動 (2010)
  • Author(s): 瀬片純市
  • Organizer: 日本数学会2010年度年会
  • Place of Presentation: 慶応義塾大学
  • Year and Date: 2010-03-27
• [Presentation] KdV, nonlinear Schrodinger equations-I, II
  • Author(s): Jun-ichi Segata
  • Organizer: NCTS/CMMSC Seminar on PDEs, Theory and Applications
  • Place of Presentation: National Chiao Tung University (Taiwan)
  • Invited