2013 Fiscal Year Final Research Report
Toward a Global Analysis for Nonlinear System of Partial Differential Equations
| Project/Area Number |
23540253
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Kyoto University (2012-2013)
Waseda University (2011) |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| Keywords | 大域的解析 / 非線形偏微分方程式 / 力学系 / 熱対流問題 / 圧縮性粘性熱伝導性流体 / Jauslin-Kreiss-Moser モデル |
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| Research Abstract |
Heat convection problems of compressible, viscous and heat-conductive fluids are investigated. Stationary bifurcations are proved to occur from the equilibrium state ( heat conduction solution ), when the Rayleigh number exceeds the critical value. They correspond to the pattern formation of the roll-type solution, the hexagonal cell and the mixed type solution. The bifurcation occurs uniformly with respect to the parameter which corresponds to the gradient of temperature and they converge to those of the Oberbeck-Boussinesq equation as the parameter tends to zero.
Jauslin-Kreiss-Moser model of Hamilton Mechanics is investigated. It is a periodically forced Burgers equation with the periodic boundary condition.
The periodic in time solutions are constructed by the Lax-Friedrichs scheme and the periodic, chaotic solutions and the Aubry-Mather set are obtained numerically.
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