Mathematical analysis and numerical computation of nonlinear partial differential equations
| Project/Area Number |
08454028
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
解析学
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| Research Institution | KYOTO UNIVERSITY |
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Principal Investigator |
OKAMOTO Hisashi RIMS,KYOTO UNIVERSITY Professor, 数理解析研究所, 教授 (40143359)
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| Co-Investigator(Kenkyū-buntansha) |
TAKEI Yoshitsugu RIMS,KYOTO UNIVERSITY Assistant Professor, 数理解析研究所, 助教授 (00212019)
MUROTA Kazuo RIMS,KYOTO UNIVERSITY Professor, 数理解析研究所, 教授 (50134466)
MIWA Tetsuji RIMS,KYOTO UNIVERSITY Professor, 数理解析研究所, 教授 (10027386)
KASHIWARA Masaki RIMS,KYOTO UNIVERSITY Professor, 数理解析研究所, 教授 (60027381)
KAWAI Takahiro RIMS,KYOTO UNIVERSITY Professor, 数理解析研究所, 教授 (20027379)
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| Project Period (FY) |
1996
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| Project Status |
Completed (Fiscal Year 1996)
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| Budget Amount *help |
¥5,900,000 (Direct Cost: ¥5,900,000)
Fiscal Year 1996: ¥5,900,000 (Direct Cost: ¥5,900,000)
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| Keywords | Equations of motion of fluids / singular perturbation / algebraic analysis / matroid theory / vortex sheet / numerical method |
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| Research Abstract |
H.Okamoto discovered some new exact solutions of the Navier-Stokes equations which shed light on the singular perturbation analysis of the equations. One of them is a generalization of stagnation-point flows of Tamada and Dorrepaal which converges on a wall obliquely. Other solutions include those solutions which satisfy Leray's similarity equations. Among others, he found those solutions which are represented by the confluent hyper-geometric functions. He also studied the stability of certain stationary Navier-Stokes equations which satisfy the inflow / outflow boundary condition. Some the solutions are proved to be stable for all the Reynolds number, which is a surprising results. By the vortex method, Okamoto and Sakajo computed numerically the vortex sheet in shear flows. Some interesting interactions between vortex sheet and shear are discovered.
T.Kawai and Y.Takei studied, via the algebraic analysis method, a certain aspect of singular perturbation theory of the Painleve equations. Their theory will be published in their book entitled "Algebraic Analysis of Singular Perturbation" (in Japanese) from Iwanami Shoten.
K.Murota and S.Iwata made a contribution to the present study through the theory of numerical linear algebra. Some singular perturbation problem leads to a very ill-conditioned matrix problem after a suitable discretization. The techniques developed by them are very helpful when we solve such ill-conditioned matrix problem. Murota proposes many methods which leads to better accuracy and speed-up of the computation.
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Report
(2 results)
Research Products
(20 results)
