Project/Area Number  09640170 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
解析学

Research Institution  Kanazawa University 
Principal Investigator 
OMATA Seiro Kanazawa University, Departmnet of Science, Associate Professor, 理学部, 助教授 (20214223)

CoInvestigator(Kenkyūbuntansha) 
GOTO Shunichi Kanazawa University, Department of Science, Associate Professor, 理学部, 助教授 (30225651)
児玉 秋雄 金沢大学, 理学部, 教授 (20111320)
FUJIMOTO Hirotaka Kanazawa University, Department of Science, Professor, 理学部, 教授 (60023595)
ICHINOSE Takashi Kanazawa University, Graduate School of Natural Science, Professor, 自然科学研究科, 教授 (20024044)
HAYASIDA Kazuya Kanazawa University, Graduate School of Natural Science, Professor, 自然科学研究科, 教授 (70023588)
TAMURA Hiroshi Kanazawa University, Department of Science, Associate Professor, 理学部, 助教授 (80188440)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥3,600,000 (Direct Cost : ¥3,600,000)
Fiscal Year 1998 : ¥1,400,000 (Direct Cost : ¥1,400,000)
Fiscal Year 1997 : ¥2,200,000 (Direct Cost : ¥2,200,000)

Keywords  Free boundary problem / Variational problem / Nonlinear partial differential equations / Numerical Analysis / Minimizing methods / Superconductivity / Liquid crystals / 自由境界問題 / 変分問題 / 非線形偏微分方程式 / 数値解析 / 最小化法 / 超伝導 / 液晶 
Research Abstract 
We mainly investigated a free boundary problem related to a variational problem. Since our problem has a feature (hat the free boundary is a set of singular points of a minimizer and the energy concentrate on it. So, we can cosider that our purpose is on treating the energy concentration phenomena on the singularity of solutions. In this stand point of view, we treated the following type of problems : (1)Develop Regularity theory of elliptic free boundary problem related to minimizing functional with moving boundary, (2)Develop a Numerical method via a minimization process, (3)Develop a method related to solve a hyperbolic free boundary problem. For problem (1), in 2dimensional case, we successfully showed regularity of free boundary on some nonlinear case. For (2), we treated the GinzburgLandau functional which mainly appear in superconducting phenomema. In this, we developed a method due to discrete Morse semiflow for parabolic and hyperbolic problems. For (3), we constucted a strong solutions related to hyperbolic free boundary problems under some compatibility conditions. Moreover we developed a software to solve this with good accuracy. We summed up these results into 7 papers (appeared or in press) and I preprint (submitted).
