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.
Authors with CRIS profile
Martin Gugat
Naturwissenschaftliche Fakultät
Günter Leugering
Lehrstuhl für Angewandte Mathematik
Simona Oana Tamasoiu
Lehrstuhl für Angewandte Mathematik
Involved external institutions
China (CN)How to cite
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://dx.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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