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


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.


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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