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Chinese Annals of Mathematics, Series B

, Volume 33, Issue 4, pp 479–500 | Cite as

H 2-stabilization of the Isothermal Euler equations: a Lyapunov function approach

  • Martin GugatEmail author
  • Günter Leugering
  • Simona Tamasoiu
  • Ke Wang
Article

Abstract

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.

Keywords

Boundary control Feedback stabilization Quasilinear hyperbolic system Balance law Gas dynamics Isothermal Euler equations Exponential stability, Lyapunov function H2-norm Stationary state Characteristic variable 

2000 MR Subject Classification

76N25 35L50 93C20 

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Copyright information

© Fudan University and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Martin Gugat
    • 1
    Email author
  • Günter Leugering
    • 1
  • Simona Tamasoiu
    • 1
  • Ke Wang
    • 1
    • 2
  1. 1.Department of MathematicsFriedrich-Alexander UniversityErlangenGermany
  2. 2.School of Mathematical SciencesFudan UniversityShanghaiChina

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