| Project/Area Number |
60460005
|
|---|
| Research Category |
Grant-in-Aid for General Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
解析学
|
|---|
| Research Institution | HIROSHIMA UNIVERSITY |
|---|
Principal Investigator |
OHARU Shinnosuke Professor, Faculty of Science, Hiroshima University, 理学部, 教授 (40063721)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
ITANO Mitsuyuki Professor, Faculty of Integrated Arts and Sciences, Hiroshima University, 総合科学部, 教授 (80034544)
TOTOKI Haruo Professor, Faculty of Science, Hiroshima University, 理学部, 教授 (70027366)
MIMURA Masayasu Professor, Faculty of Science, Hiroshima University, 理学部, 教授 (50068128)
MAEDA Fumi-Yuki Professor, Faculty of Science, Hiroshima University, 理学部, 教授 (10033804)
KUSANO Takasi Professor, Faculty of Science, Hiroshima University, 理学部, 教授 (70033868)
|
|---|
| Project Period (FY) |
1985 – 1986
|
| Project Status |
Completed (Fiscal Year 1986)
|
| Budget Amount *help |
¥5,300,000 (Direct Cost: ¥5,300,000)
Fiscal Year 1986: ¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 1985: ¥2,900,000 (Direct Cost: ¥2,900,000)
|
|---|
| Keywords | Initial-Boundary Value Problems for Nonlinear Evolution Systems / Reaction-Diffusion Systems / Free Boundary Problem / Time-Dependent Evolution Equation / Nonlinear Evolution Operator / Semilinear Evolution Equation / Nonlinear Perturbations / 非線形関数解析 |
|---|
| Research Abstract |
In this research project the general theory of nonlinear evolution equations was discussed and various nonlinear problems were studied comprehensively from the viewpoints of the theory of ordinary differential equations, that of partial differential equations, nonlinear functional analysis, probability theory and geometry. The participant investigators were divided into five research groups and, with this Grant-in-Aid for Scientific Research from the Ministry of Education, each group has obtained a large number of remarkable results according to the respective research objects.
The first group made researches in differential equations involving various types of nonlinear terms and brought about lots of significant results concerning the existence, regularity, singularity, asymptotic behavior and stability of the solutions. The second group treated a variety of nonlinear problems which arose in mathematical sciences. Members of the group exploited new methods for constructing the solutions and are now engaged in studies on qualitative properties as well as precise behavior of the solutions. The third group studied the infinite dimensional diffusion processes and obtained new results on isomorphism problems in ergodic theory.
The fourth group made a study of geometric properties of normed spaces in terms of orthogonality in a generalized sense. Some members of the group presented interesting resuts on the change of variables to distributions. Finally, the fifth group succeeded in finding a general and very natural class of nonlinear evolution operators in Banach spaces and investigated the detailed properties of evolution operators of the class. Members of the group established three types of generation theories for such evolution operators and applied them to typical nonlinear differential equations.
|
