Asymptotic analysis on the Euler Poisson equation arising in plasma physics

2014 Fiscal Year Final Research Report

• Project/Area Number: 23654062
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Global analysis
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: SHINYA Nishibata 東京工業大学, 情報理工学(系)研究科, 教授 (80279299)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: オイラー方程式 / ポアソン方程式 / 双曲型保存則 / ボーム・シース条件 / 境界層

Outline of Final Research Achievements

We proved the asymptotic stability of the stationary solution to an Euler Poisson equation arising in the plasma physics under the Bohm sheath condition.　We also obtained the convergence rate towards the stationary solution subject to the initial condition. In addition we made numerical experiments. Precisely, we confirmed numerically that the solution converges to the stationary solution as time tends to infinity. Here we compared several numerical schemes. In conclusion, we see that the roe scheme makes a best performance in stability of scheme and convergence speed.

Free Research Field

非線形偏微分方程式論