Project/Area Number  09640207 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
解析学

Research Institution  Fukuoka University 
Principal Investigator 
YAMADA Naoki Fukuoka Univ., Fac. of Science, Professor, 理学部, 教授 (50030789)

CoInvestigator(Kenkyūbuntansha) 
KUROKIBBA Masaki Fukuoka Univ., Fac. of Sci., Res. Assist., 理学部, 助手 (60291837)
ISHII Katsuyuki Kobe Univ. of Mercantile Marine, Fac. of Marcantile Marine Sci., Associate Professor, 商船学部, 助教授 (40232227)
KUSANO Takashi Fukuoka Univ., Fac. of Sci. , Prof., 理学部, 教授 (70033868)

Project Fiscal Year 
1997 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥2,900,000 (Direct Cost : ¥2,900,000)
Fiscal Year 1999 : ¥1,000,000 (Direct Cost : ¥1,000,000)
Fiscal Year 1998 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1997 : ¥1,100,000 (Direct Cost : ¥1,100,000)

Keywords  obstacle problem / Viscosity solutions / Crystalline curvature / 障害物問題 / 粘性解 / クリスタライン曲率 / 相分離 / 走化性方程式系 / 球対称解 
Research Abstract 
We formulated obstacle problems especially bilateral obstacle problems by the framework of viscosity solutions, and obtained an estimate of the size of touching subdomains of the solution. This estimate is an extension of the previous works that estimated the size of touching subdomains for unilateral obstacle problems. The motion of polygons governed by crystalline curvature is a model of crystal growth under the super cooling. We consider a twodimensional problem with a crystalline energy whose level sets are regular npolygons and got an result of the convergence of these solutions to the unique smooth solution of the mean curvature flow. We also investigate a system of partial differential equations associated with the free energy of surface tension. This system is proposed as a model of phase separation phenomena in alloy of two metals. We proved the global existence and the uniqueness of the solution. We considered various nonlinear ordinary differential equations and got conditions that the solutions to be oscillatory or nonoscillatory. These investigations are not only interesting in itself but also useful to construct approximate solutions in partial differential equations treated in our project.
