Mathematical study to Defect travelling wave in dicipative system

• Project/Area Number: 22540136
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Hiroshima University
• Principal Investigator: OHNISHI Isamu 広島大学, 大学院・理学研究科, 准教授 (30262372)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2010: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 散逸系 / 非可磧分系 / 進行波解 / パターン形成 / 散逸構造 / 進行波 / パルス / 大偏差原理 / 反応拡散系 / 変分構造 / 移動境界

Research Abstract

Bifurcation analysis to Lugiato-Lefever equation to get desired pattern with use of reduction to center manifold theory. Fine analysis to bifurcation equation leads us to rigorous proof to existence of the secondary bifurcation. Mathematically rigorous analysis to pattern which causes the desired travelling wave. Experiment and numerical simulation to travelling wave in Sol=Gel system and theoretical analysis to it.

Research Products

• [Journal Article] Stability of Stationary Solution for the Lugiato-Lefever Equation (2011)
  • Author(s): T.Miyaji,I.Ohnishi,Y.Tsutsumi
  • Journal Title: Tohoku Math. Journal Volume: 63 Pages: 651-663
  • NAID: 110008764865
  • Peer Reviewed
• [Journal Article] Stability of a stationary solution for the Lugiato-Lefever equation (2011)
  • Author(s): Miyaji, Ohnishi, Tsutsumi
  • Journal Title: 東北数学雑誌(Tohoku Math.Journal)(Centennial Issue) Volume: Vol.63 No.4(招待論文) Pages: 651-663
  • NAID: 110008764865
  • Peer Reviewed
• [Journal Article] Takamatsu Mathematical analysis to coupled oscillators system with conservation law (2010)
  • Author(s): T.Miyaji, I. Ohnishi, R. Kobayasi A.
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: 21 Pages: 129-147
  • Peer Reviewed
• [Journal Article] Bifurcation analysis to the Lugiato-Lefever equation in one space dimension (2010)
  • Author(s): T.Miyaji,I.Ohnishi,Y.Tsutsumi
  • Journal Title: Physica D Volume: 239 Pages: 2066-2083
  • Peer Reviewed
• [Presentation] Bifurcation analysis to Lugiato-Lefever equation (2012)
  • Author(s): I.Ohnishi
  • Organizer: JISD2012
  • Place of Presentation: (Universitat Politecnica de Catalunya) Barcelona, (Spain)
  • Year and Date: 2012-05-30
• [Presentation] Bifurcation analysis to Lugiato-Lefever equation (2011)
  • Author(s): I.Ohnishi
  • Organizer: 九州大学物理学教室談話会
  • Place of Presentation: 九州大学 箱崎キャンパス
  • Year and Date: 2011-12-15
• [Presentation] Bifurcation analysis to Lugiato-Lefever equation in One space dimension (2011)
  • Author(s): 大西勇
  • Organizer: Equadiff 2011 in U.K.
  • Place of Presentation: Loughborough University(UK)
  • Year and Date: 2011-08-05
• [Presentation] Bifurcation analysis to Lugiato-Lefever equation (2011)
  • Author(s): I.Ohnishi
  • Organizer: SIAM conference
  • Place of Presentation: Snowbird, Utah, USA
  • Year and Date: 2011-05-25
• [Presentation] Pattern formation analysis to Cahn-Hilliard type equation related to Sol-Gel phase separation (2010)
  • Author(s): I.Ohnishi
  • Place of Presentation: 岩手大学
  • Year and Date: 2010-12-15
• [Presentation] A Mathematical analysis to Liesegang ring as a radially symmetric solution in n-space dimension (2010)
  • Author(s): I.Ohnishi
  • Organizer: the 6th EASIUM and AMIC 2010
  • Place of Presentation: クアラルンプール マレーシア
  • Year and Date: 2010-06-23
• [Presentation] Bifurcation analysis to LL equation in one space dimension (2010)
  • Author(s): 大西勇
  • Organizer: AIMS conference
  • Place of Presentation: ドレスデン(ドイツ)(招待講演)
  • Year and Date: 2010-05-27
• [Book] 生物数学入門 (2011)
  • Author(s): Linda J.S. Allen
  • Total Pages: 440
  • Publisher: 共立出版
• [Book] 生物数学入門 (2011)
  • Author(s): 竹内、佐藤、守田、宮崎, ら監訳の5章の半分くらいを担当
  • Publisher: 共立出版
• [Remarks] は、記念号のため、特別なページがあったので、書いておきます。
  • URL: http://www.math.tohoku.ac.jp/tmj/TMJ100issue.html