New development of pattern dynamics in reaction-diffusion equations on metric graphs

• Project/Area Number: 25K07142
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12040:Applied mathematics and statistics-related
• Research Institution: Ryukoku University
• Principal Investigator: 森田 善久 龍谷大学, 公私立大学の部局等, 研究員 (10192783)
• Co-Investigator(Kenkyū-buntansha): 石井 宙志 北海道大学, 電子科学研究所, 助教 (20966337)
• Project Period (FY): 2025-04-01 – 2028-03-31
• Project Status: Granted (Fiscal Year 2025)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2027: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2026: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2025: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 反応拡散方程式 / メトリックグラフ / 全域解 / パターンダイナミクス / フロント波の伝播

Outline of Research at the Start

We aim to establish a unified approach and a method for classifying front entire solutions to the bistable reaction-diffusion equation on tree graphs composed of half-lines. Moreover, we develop a method to control the movement of localized patterns in reaction-diffusion systems at branching points.