Applied analysis for nonlinear problems
| Project/Area Number |
15K21369
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical analysis
Foundations of mathematics/Applied mathematics
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| Research Institution | Keio University |
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Principal Investigator |
SOGA Kohei 慶應義塾大学, 理工学部(矢上), 専任講師 (80620559)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | Hamilton力学系 / Hamilton-Jacobi方程式 / 粘性解 / 弱KAM理論 / Navier-Stokes方程式 / 最大正則性 / Leray-Hopfの弱解 / 差分法 / discount 近似 / 有限差分法 / 収束証明 / 誤差評価 / discount近似 / 二相自由境界問題 / 適切性 / modeling |
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| Outline of Final Research Achievements |
(1) We studied Hamiltonian dynamics and Hamilton-Jacobi equations in terms of weak KAM theory. We formulated a version of weak KAM theory for discounted Hamilton-Jacobi equations and applied it to quantitative analysis of the vanishing discount limit. We also prepared necessary mathematical concepts in order to construct a version of weak KAM theory for discretized Hamilton-Jacobi equations.
(2) We did mathematical analysis on two phase flows of compressible fluids in terms of the maximal regularity. We also presented a numerical method of incompressible fluids and proved its convergence.
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| Academic Significance and Societal Importance of the Research Achievements |
(1) discount近似および差分近似されたHamilton-Jacobi方程式に対して弱KAM理論の枠組みを与えることで、同研究分野の理論的・数値解析的方法のさらなる発展に貢献した。
(2) 自由境界を持つNavier-Stokes方程式の厳密な数学解析行うと同時に、流体力学における数値計算の数学的正当性を保証する理論を構築することで、同研究分野の理論的・数値解析的方法のさらなる発展に貢献した。
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Report
(5 results)
Research Products
(11 results)
