| Project/Area Number |
09640297
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | MEIJI UNIVERSITY |
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Principal Investigator |
FUJITA Hiroshi Meiji Univ.Dept.of Math.Professor, 理工学部, 教授 (80011427)
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| Co-Investigator(Kenkyū-buntansha) |
KAWARADA Hideo Chiba Univ.Dept.of Appl.Math Professor, 工学部, 教授 (90010793)
KATSURADA Masashi Meiji Univ.Dept.of Math.Lecturer, 理工学部, 講師 (80224484)
FURUHASHI Rohzo Meiji Univ.Dept.of Math.Professor, 理工学部, 教授 (40061973)
KONNO Reiji Meiji Univ.Dept.of Math.Professor, 理工学部, 教授 (20061921)
MORIMOTO Hiroko Meiji Univ.Dept.of Math.Professor, 理工学部, 教授 (50061974)
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| Project Period (FY) |
1997 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 1998: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 1997: ¥1,900,000 (Direct Cost: ¥1,900,000)
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| Keywords | Stokes Equation / Variatinal Inequality / Uzawa Algorithm / Domain Decomposition Method / inf-sup Condition / General Outflow Condition / Navier-Stokes Equation / Boundary Condition of Friction Type / 非線形 / 摩擦型境界条件 / 領域分割 / ポアッソン方程式 |
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| Research Abstract |
The main results of our study are as follows.
1. Boundary Conditions of Frictional Type
The basic mathematical problem for stationary Stokes flow under the boundary condition for friction type has been solved by the kead investigator when he gave a series of lectures at College de France in 1993, by use of the theory of Variation Inequalities. As a result of the present study, a certain saddle-point search formulation of the problem has been developed, which regards the pressure as a kind of Lagrange multiplier. As a consequence, we have obtained a better convergence theory for the Uzawa algorithms applied to these nonlinear problems.
2. Mathematical Study of DDM
In 1994, the head investigator proposed a new method to analyze the convergence speed of iterations arising from the domain decomposition method for elliptic equations , which yields a kind of optimal rates of convergence under certain geometrical assumtions on the relationship among sub-domains. Through the present study, a young collaborator, Norikazu Saito has succeeded to strengthen this method, which is sometimes called Fujita's method, so that the Stokes equation can be dealt with nicely. Saito makes use of some crucial estimates based on the so-called inf-supcondition for sub-domains.
3.Solvability of the Navier-Stokes Equation under General Outflow Condition
The head investigator has succeeded in proving, by means of a constructive a priori estimate, the solvability of the 2-dimensional and "symmetric "boundary value problems for the stationary Navier-Stokes flows under the general outflow (flux) condition. The crucial step of the proof might be called the method of virtual drains. Some nontrivial generalizations have been made by the head investigator and another investigator Hiroko Morimoto.
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