Study of traveling wave and interfacial dynamics in nonlinear diffusion equation

Research Project

Project/Area Number	16K05245
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Multi-year Fund
Section	一般
Research Field	Mathematical analysis
Research Institution	Kyoto Sangyo University
Principal Investigator	Yagisita Hiroki 京都産業大学, 理学部, 教授 (80349828)
Project Period (FY)	2016-04-01 – 2021-03-31
Project Status	Completed (Fiscal Year 2020)
Budget Amount *help	¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000) Fiscal Year 2020: ¥130,000 (Direct Cost: ¥100,000、Indirect Cost: ¥30,000) Fiscal Year 2019: ¥130,000 (Direct Cost: ¥100,000、Indirect Cost: ¥30,000) Fiscal Year 2018: ¥130,000 (Direct Cost: ¥100,000、Indirect Cost: ¥30,000) Fiscal Year 2017: ¥130,000 (Direct Cost: ¥100,000、Indirect Cost: ¥30,000) Fiscal Year 2016: ¥130,000 (Direct Cost: ¥100,000、Indirect Cost: ¥30,000)
Keywords	非線形現象 / 非線形解析学 / 非線形偏微分方程式 / 非線形解析 / 拡散方程式
Outline of Final Research Achievements	We studied the dynamics of traveling waves and interfaces with respect to parabolic equations that describe nonlinear diffusion phenomena. In particular, it is natural to think of the space in which traveling waves and curved states live as an infinite dimensional space, and as a result of studying such an infinite dimensional space, many infinite dimensional spaces and many finite dimensional spaces have been found. We found a universal structure to share, and in the process extracted a universal method of interpreting mathematical statements.
Academic Significance and Societal Importance of the Research Achievements	非線形系の拡散現象は、物理学、化学、生物学、さらに近年は金融工学上のモデル等、多くの分野で現れる。それらの中には、急激な状態変化が狭い領域に集中する界面と呼ばれる局在構造が出現して、この界面の示す振る舞いを理解することが非線形現象を解明する上での鍵になることが数多くある。本研究による成果は、そのような理解を可能にするための数学的な基礎の提供に資することが大いに期待できるものである。