Obstacle problem for fluid mechanics and parabolic variational inequalities

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400164
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Kyoto University of Education
• Principal Investigator: Fukao Takeshi 京都教育大学, 教育学部, 教授 (00390469)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 発展方程式 / 体積制約条件 / 力学的境界条件 / 動的境界条件 / 放物型方程式

Outline of Final Research Achievements

We consider the well-posedness for an abstract parabolic variational inequality with some volume constraint. Using the abstract theory for operator inclusion of subdifferential which is related to the volume constraint on some Banach space, we can obtain the suitable well-posedness results for Allen-Cahn equation or Cahn-Hilliard system with dynamic boundary conditions. As the gift of this treatment, we can find an interesting problem of equation and dynamic boundary condition of Cahn-Hilliard type, and then, we also prove the well-posedness of this kind of Cahn-Hilliard system.

Free Research Field

発展方程式論