Project/Area Number  09304016 
Research Category 
GrantinAid for Scientific Research (A)

Section  一般 
Research Field 
解析学

Research Institution  Osaka University, Graduate School of Sciences 
Principal Investigator 
IKAWA Mitsuru Graduate School of Sciences, Osaka Univ., Professor, 大学院・理学研究科, 教授 (80028191)

CoInvestigator(Kenkyūbuntansha) 
ISOZAKI Hiroshi Graduate School of Sciences, Osaka University, Assoc.Prof., 大学院・理学研究科, 助教授 (90111913)
NISHITANI Tatsuo Graduate School of Sciences, Osaka Univ., Professor, 大学院・理学研究科, 教授 (80127117)
上見 練太郎 北海道大学, 大学院・理学研究科, 教授 (10000845)
ICHINOSE Takashi Graduate School of Nat.Sci., Kanazawa Univ., Professor, 大学院・自然科学研究科, 教授 (20024044)
YAJIMA Kenji Graduate School of Math.Sci., Univ.of Tokyo Professor, 大学院・数理科学研究科, 教授 (80011758)
MATSUMURA Akitaka Graduate School of Sciences, Osaka Univ., Professor, 大学院・理学研究科, 教授 (60115938)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥16,100,000 (Direct Cost : ¥16,100,000)
Fiscal Year 1998 : ¥5,800,000 (Direct Cost : ¥5,800,000)
Fiscal Year 1997 : ¥10,300,000 (Direct Cost : ¥10,300,000)

Keywords  differential equations / evolution equations / hypoellicptic / scattering / inverse problems / Dirac operator / 微分方程式 / 発展方程式 / 準楕円性 / 散乱理論 / 逆問題 / Dirac作用素 / 双曲型方程式 / 力学系 / 周期解 / schroedinger方程式 / 可積分系 
Research Abstract 
We studied differential equations, in the range from ordinary differential equations to partial differential equations and from linear ones to nonlinear ones. We cooperated with the Division of Functional Equations, Mathematical Scociety of Japan. As the result of a study including all the researchers of this field in Japan, we clarified the tendency of the forcecoming subjects. As one of the main results of our synthetic research, Atsushi Yagi published a monograph on evolution equations in Banach spaces. His theory made possible a systematic treatment of nonlinear problems in a form of evolution equations in Banach spaces. One point we want to emphasize is that his theory includes degenerate problems. As to another main subject of research, scattering theory, the Head of Investigaor is writing a monograph which represents the results of synthetic studies of partial differential equations related to scattering theory. Other subject, for instance, hypoellipticity of equations, by the studies in the space of analytic functions or of Gevrey class, the meanings of the conditions posed up to now has been made clear. In ordinary differential equations, by the studies of asymptotic behaviors of hypergeometric functions of congruent type made clear the structure of solutions. As to inverse problems of scattering problems, which are important even in the engineering, a theorem which guarantees the indentification of scatterers from scattering informations of a fixed enegy. We prepared the synthetic discussions on differential equations, but could not reach to results which sythesize the many subject of differential equations.
