2002 Fiscal Year Final Research Report Summary
Study on the global behavior of solutions for the fluid equation
| Project/Area Number |
13640206
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | HITOTSUBASHI UNIVERSITY |
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Principal Investigator |
ISHIMURA Naoyuki HitotsubashiUniversity, Graduate School of Economics, Associate Professor, 大学院・経済学研究科, 助教授 (80212934)
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| Co-Investigator(Kenkyū-buntansha) |
TAKAOKA Koichiro HitotsubashiUniversity, Graduate School of Commerce, Lecturer, 大学院・商学研究科, 講師 (50272662)
YAMAZAKI Masao Waseda University, Department of Mathematics, Professor, 理工学部, 教授 (20174659)
MORIMOTO Hiroko Meiji University, Department of Mathematics, Professor, 理工学部, 教授 (50061974)
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| Project Period (FY) |
2001 – 2002
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| Keywords | Blasius equation / Boundary layer theory / blowing-up solutions / Free boundary problems / Mathematical Finance |
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| Research Abstract |
We have undertaken our research projects mainly on the following two subjects.
(1) Results are obtained for the analysis on the structure of solutions to the steady state of the Kuramoto-Sivashinsky (KS) equation and/or to the Blasius equation. Both equations are related to the fluid dynamics and have the similar third-order differential operator. By use of the monotonicity, the reduction of the third-order equation into the second-order one is performed. In view of this reduction, the existence of blowing-up solutions for the steady state of the KS equation is proved. These kind of solutions have not been mentioned in the literature so far. Moreover, an elementary existence proof of blowing-up solutions for the Blasius equation is also given, which may shed light on the validity of the Blasius equation itself with regard to the Prandtl boundary layer theory.
(2) Free boundary problems arise in a wide variety of nonlinear sciences, including one-phase fluid flow problem. Here we are concerned with the pricing of American put option. We present an exact integral formula for the solution.
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