Large time structure of coupled system of hyperbolic and elliptic equations

2015 Fiscal Year Final Research Report

• Project/Area Number: 22340027
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: Nishibata Shinya 東京工業大学, 情報理工学(系)研究科, 教授 (80279299)
• Co-Investigator(Kenkyū-buntansha): Matsumura Akitaka 大阪大学, 情報科学研究科, 名誉教授 (60115938)
• Project Period (FY): 2010-04-01 – 2016-03-31
• Keywords: オイラー方程式 / ポアソン方程式 / 双曲型保存則 / 定常解 / 境界層 / プラズマ / シース / 半導体

Outline of Final Research Achievements

We proved that a monotone stationary solution to the Euler-Poisson equations arising in Plasma physics is time asymptotically stable on mulch-dimensional half space. Moreover, we obtained the convergence rate, as time tends to infinity, subject to the initial　condition. We gave the mathematical justification of the relaxation time limits in hydrodynamic models for semiconductor and made clear the hierarchy among several semiconductor model equations.For the general system of hyperbolic-parabolic coupled equations, we proved the existence and the time asymptotic stability of the stationary solution. We also obtained the convergence rate subject to the initial condition.

Free Research Field

非線形偏微分方程式