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

Gugat M, Leugering G, Tamasoiu SO, Wang K (2012)


Publication Language: English

Publication Status: Published

Publication Type: Journal article

Publication year: 2012

Journal

Publisher: World Scientific Publishing / Springer Verlag (Germany)

Book Volume: 33

Pages Range: 479-500

Journal Issue: 4

URI: http://link.springer.com/article/10.1007/s11401-012-0727-y

DOI: 10.1007/s11401-012-0727-y

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.

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APA:

Gugat, M., Leugering, G., Tamasoiu, S.O., & Wang, K. (2012). H (2)-stabilization of the Isothermal Euler equations: a Lyapunov function approach. Chinese Annals of Mathematics Series B, 33(4), 479-500. https://doi.org/10.1007/s11401-012-0727-y

MLA:

Gugat, Martin, et al. "H (2)-stabilization of the Isothermal Euler equations: a Lyapunov function approach." Chinese Annals of Mathematics Series B 33.4 (2012): 479-500.

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