| Project/Area Number |
26800067
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Mathematical analysis
|
|---|
| Research Institution | Nagoya Institute of Technology (2015-2018)
Tokyo Institute of Technology (2014) |
|---|
Principal Investigator |
Suzuki Masahiro 名古屋工業大学, 工学(系)研究科(研究院), 准教授 (30587895)
|
|---|
| Research Collaborator |
Takayama Masahiro
|
|---|
| Project Period (FY) |
2014-04-01 – 2019-03-31
|
| Project Status |
Completed (Fiscal Year 2018)
|
| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
|
|---|
| Keywords | シース / Bohm条件 / Euler-Poisson方程式 / 定常解 / 3 次元円環領域 / 摂動半空間 / プラズマ / Euler-Poisson 方程式 / 球面対称解 / 球面対称定常解 / 一般化された Bohm 条件 / 平面定常解 / 安定性 |
|---|
| Outline of Final Research Achievements |
A boundary layer called a sheath appears around the wall where the plasma contacts. H. Bohm considered a plasma composed of electrons and a single kind of positive ion, and derive the Bohm condition for the formation of a sheath. Furthermore, K.-U. Riemann considered a plasma composed of electrons and various positive ions, and proposed the generalized Bohm condition. The motions of these plasmas can be described by the Euler-Poisson equation, and it can be understood that the sheath is a steady solution of the equation. We analyzed the existence and stability of the stationary solution under those Bohm conditions.
|
| Academic Significance and Societal Importance of the Research Achievements |
EP 方程式から形式的に導出された Bohm 条件に対して，数学的に厳密な正当性を与えるなど，シースに関する数学理論を完成させることはシース現象の理解を深める助けとなろう. また, EP 方程式は双曲・楕円型連立方程式系に分類されるが，半導体中の電子流，熱輻射気体，自己重力をもつガス惑星などの現象を記述するモデルも双曲・楕円型連立系である．本研究で得られた解析手法は他のモデルにも応用可能であり，これらの数理物理モデルを一般化した双曲・楕円型連立系の数学理論を構築する契機となろう．
|
