2014 Fiscal Year Final Research Report
Mathematical analysis on hyperbolic-elliptic systems arising in semiconductor engineering and plasma physics
Project/Area Number |
23740111
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Basic analysis
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Research Institution | Tokyo Institute of Technology |
Principal Investigator |
SUZUKI Masahiro 東京工業大学, 情報理工学(系)研究科, 助教 (30587895)
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Project Period (FY) |
2011-04-28 – 2015-03-31
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Keywords | Hydrodynamic model / Drift-diffusion model / Euler-Poisson equations / 安定性解析 / 漸近解析 |
Outline of Final Research Achievements |
We analyzed the drift- diffusion model for semiconductors over rectangle domains adopting the Dirichlet- Neumann mixed boundary condition. The stability of stationary solutions was proved for the situation that a direct current voltage is applied to semiconductors. Moreover, we showed the unique existence and the stability of the time-periodic solution if a alternating current voltage is applied. We study the Euler-Poisson equations, which describes the motion of plasma, over a half space. It is shown that the generalized Bohm criterion give a sufficient condition for the existence and the stability of stationary solutions to the Euler-Poisson equations.
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Free Research Field |
非線形偏微分方程式
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