Mathematical approach for spatial pattern in combustion

• Project/Area Number: 21840047
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: Meiji University
• Principal Investigator: IKEDA Kota Meiji University, 研究・知財戦略機構, 講師 (50553369)
• Project Period (FY): 2009 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000); Fiscal Year 2010: ¥988,000 (Direct Cost: ¥760,000、Indirect Cost: ¥228,000); Fiscal Year 2009: ¥1,092,000 (Direct Cost: ¥840,000、Indirect Cost: ¥252,000)
• Keywords: 関数方程式論 / 応用数学 / 反応拡散方程式系 / 進行波解 / 安定性 / fingering pattern / 退化型非線形項

Research Abstract

1. We construct a traveling wave solution in a reaction-diffusion model with three components for combustion. We prove the stability of the solution in higher dimension. We reduce our system to a reaction-diffusion system with two components. 2. We derive a differential equation which defines a function to characterize a spiky pattern in a degenerate reaction-diffusion equation. Our paper will be published in a journal.

Research Products

• [Journal Article] Travelling wave of a 3-component reaction-diffusion model in smoldering combustion (2011)
  • Author(s): Kota Ikeda, Masayasu Mimura
  • Journal Title: Communications on Pure and Applied Analysis Pages: 1-32
  • Peer Reviewed
• [Journal Article] DYNAMICS OF A BOUNDARY SPIKE FOR THE SHADOW GIERER-MEINHARDT SYSTEM (2010)
  • Author(s): Shin-Ichiro Ei, Kota Ikeda, Yasuhito Miyamoto
  • Journal Title: Communications on Pure and Applied Analysis Pages: 1-31
  • NAID: 120005324438
  • Peer Reviewed
• [Journal Article] Travelling wave of a 3-component reaction-diffusion model in smoldering combustion
  • Author(s): Kota Ikeda, Masayasu Mimura
  • Journal Title: Communications on Pure and Applied Analysis Volume: (accepted)
  • Peer Reviewed
• [Presentation] 縮約方程式が現れる反応拡散系に関する解析 (2010)
  • Author(s): 池田幸太
  • Organizer: 京都駅前セミナー
  • Place of Presentation: キャンパスプラザ京都,京都市,京都
  • Year and Date: 2010-11-12
• [Presentation] Instability of multi-spots in general shadow systems for reaction-diffusion equations (2010)
  • Author(s): 池田幸太,栄伸一郎,柳田英二
  • Organizer: International Workshop on Pattern Formation in Chemical and Biological Systems
  • Place of Presentation: Eotvos Lorand University, Budapest, Hungary
  • Year and Date: 2010-10-26
• [Presentation] Reflection of a traveling wave in smoldering combustion (2010)
  • Author(s): 池田幸太,三村昌泰
  • Organizer: The 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications
  • Place of Presentation: Dresden University of Technology, Dresden, Germany
  • Year and Date: 2010-05-28
• [Presentation] Instability of multi-spots in general shadow systems for reaction-diffusion equations(ポスター発表) (2010)
  • Author(s): 池田幸太
  • Organizer: Japan-Taiwan Joint Workshop for Graduate Students in Applied Mathematics
  • Place of Presentation: National Taiwan Normal University, Taipei
  • Year and Date: 2010-03-01
• [Presentation] Reflection of a traveling wave in smoldering combustion (2009)
  • Author(s): 池田幸太,三村昌泰
  • Organizer: 微分方程式の総合的研究
  • Place of Presentation: 東京大学,東京
  • Year and Date: 2009-12-18
• [Presentation] Reflection of a traveling wave in smoldering combustion (2009)
  • Author(s): 池田幸太
  • Organizer: 微分方程式の総合的研究,関数方程式分科会,日本数学会
  • Place of Presentation: 東京大学,東京
  • Year and Date: 2009-12-18
• [Presentation] Instability of multi-spots in general shadow systems for reaction-diffusion equations (2009)
  • Author(s): 池田幸太
  • Organizer: Seminar in Mathematical department
  • Place of Presentation: National Taiwan University, Taipei
  • Year and Date: 2009-11-05
• [Presentation] Reflection of a traveling wave in smoldering combustion, Nonlinear evolution equations and mathematical modeling (2009)
  • Author(s): 池田幸太,三村昌泰
  • Organizer: Research Institute for Mathematical Sciences
  • Place of Presentation: Kyoto University, Kyoto
  • Year and Date: 2009-10-22
• [Presentation] Reflection of a traveling wave in smoldering combustion (2009)
  • Author(s): 池田幸太
  • Organizer: Nonlinear evolution equations and mathematical modeling modeling
  • Place of Presentation: Kyoto University,京都Kyoto University
  • Year and Date: 2009-10-22
• [Presentation] シャドウ系における多重スポットの不安定性と固有関数の形状 (2009)
  • Author(s): 池田幸太
  • Organizer: 2009日本数学会秋季総合分科会,関数方程式分科会,日本数学会
  • Place of Presentation: 大阪大学,大阪
  • Year and Date: 2009-09-29
• [Presentation] Pattern Formation in RD systems (2009)
  • Author(s): 池田幸太
  • Organizer: 西成研究室セミナー
  • Place of Presentation: 東京大学,東京
  • Year and Date: 2009-07-21
• [Presentation] シャドウ系における多重スポットの不安定性 (2009)
  • Author(s): 池田幸太
  • Organizer: RDSセミナー
  • Place of Presentation: 明治大学,神奈川
  • Year and Date: 2009-06-16
• [Presentation] ギーラー・マインハルト方程式に対するシャドウ系における多重スポットの不安定性 (2009)
  • Author(s): 池田幸太
  • Organizer: さいたま数理解析セミナー
  • Place of Presentation: 埼玉大学サテライトキャンパス,埼玉
  • Year and Date: 2009-05-28
• [Presentation] ギーラー・マインハルト方程式に対するシャドウ系における多重スポットの不安定性 (2009)
  • Author(s): 池田幸太
  • Organizer: 応用解析セミナー
  • Place of Presentation: 東京大学,東京
  • Year and Date: 2009-04-30
• [Presentation] ある燃焼モデルに現れる進行波解について (2009)
  • Author(s): 池田幸太
  • Organizer: HMAセミナー
  • Place of Presentation: 広島大学,広島
  • Year and Date: 2009-04-17
• [Remarks]
  • URL: http://home.mims.meiji.ac.jp/~ikeda/