Pattern formation and interfacial dynamics in nonlinear partial differential equations

• Project/Area Number: 16K05220
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Iwate University
• Principal Investigator: Nara Mitsunori 岩手大学, 理工学部, 准教授 (90512161)
• Project Period (FY): 2016-10-21 – 2019-03-31
• Project Status: Completed (Fiscal Year 2018)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2016: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 偏微分方程式 / 反応拡散方程式 / 進行波 / 界面現象 / 安定性 / 擬微分方程式 / 非線形問題 / 応用数学 / 関数方程式論

Outline of Final Research Achievements

This research mainly dealt with the following two topics; 1) generation and time evolution of spreading fronts in the Allen-Cahn equations, especially in the anisotripic Allen-Cahn equations; 2) nonlinear stability and instability of planar waves in the bidomain equaiton with bistable type nonlinearity on infinite strips.

Academic Significance and Societal Importance of the Research Achievements

本研究では，主として拡散の効果が空間的に非等方的な非線形偏微分方程式における進行波などの解析に取り組んだ。一連の研究成果は，特に生物学・医学生理学における情報伝達機構への理論面からの理解の深化，現象の解明の一助となるものである。

Research Products

• [Int'l Joint Research] ミネソタ大学(米国)
• [Int'l Joint Research] ミネソタ大学(米国)
• [Int'l Joint Research] ミネソタ大学(米国)
• [Journal Article] Asymptotic behavior of spreading fronts in the anisotropic Allen-Cahn equation on R^n (2019)
  • Author(s): Hiroshi Matano, Yoichiro Mori and Mitsunori Nara
  • Journal Title: A.I.H. Analyse non Lineaire Volume: 36 Issue: 3 Pages: 585-626
  • DOI: 10.1016/j.anihpc.2018.07.003
  • Peer Reviewed / Int'l Joint Research
• [Presentation] Stability of front solutions of the bidomain equation on a strip (2018)
  • Author(s): Mitsunori Nara
  • Organizer: The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications
  • Int'l Joint Research
• [Presentation] Asymptotic behavior of spreading fronts in the anisotropic Allen-Cahn equations on R^n (2018)
  • Author(s): 奈良光紀
  • Organizer: 南大阪応用数学セミナー
  • Invited