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| $H^2$-Stabilization of the Isothermal Euler Equations: a Lyapunov Function Approach |
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Citation： |
Martin GUGAT,Günter LEUGERING,Simona TAMASOIU,Ke WANG.$H^2$-Stabilization of the Isothermal Euler Equations: a Lyapunov Function Approach[J].Chinese Annals of Mathematics B,2012,33(4):479~500 |
| Page view： 2035
Net amount： 1330 |
Authors： |
Martin GUGAT; Günter LEUGERING; Simona TAMASOIU; Ke WANG; |
Foundation： |
the Initial Training Network “FIRST” of the Seventh Framework Programme of the European Community’s (No. 238702) and the DFG-Priority Program 1253: Optimization withPDEs (No. GU 376/7-1). |
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| 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, $H^2$-norm, Stationary state,Characteristic variable |
Classification： |
76N25, 35L50, 93C20 |
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