H 2 -stabilization of the Isothermal Euler equations: a Lyapunov function approach
作者: Martin GugatGünter LeugeringSimona TamasoiuKe Wang
作者单位: 1Department of Mathematics, Friedrich-Alexander University
2School of Mathematical Sciences, Fudan University
刊名: Chinese Annals of Mathematics, Series B, 2012, Vol.33 (4), pp.479-500
来源数据库: Springer Journal
DOI: 10.1007/s11401-012-0727-y
关键词: Boundary controlFeedback stabilizationQuasilinear hyperbolic systemBalance lawGas dynamicsIsothermal Euler equationsExponential stabilityLyapunov functionH 2 -normStationary stateCharacteristic variable
英文摘要: Abstract(#br)The authors consider the problem of boundary feedback stabilization of the 1D Euler gas dynamics locally around stationary states and prove the exponential stability with respect to the H 2 -norm. To this end, an explicit Lyapunov function as a weighted and squared H 2 -norm of a small perturbation of the stationary solution is constructed. The authors show that by a suitable choice of the boundary feedback conditions, the H 2 -exponential stability of the stationary solution follows. Due to this fact, the system is stabilized over an infinite time interval. Furthermore, exponential estimates for the C 1 -norm are derived.
全文获取路径: Springer  (合作)
影响因子:0.504 (2012)

  • stabilization 稳定
  • approach 
  • function 函数
  • Euler 欧拉