NEUMANN BOUNDARY FEEDBACK STABILIZATION FOR A NONLINEAR WAVE EQUATION: A STRICT H-2-LYAPUNOV FUNCTION
Leugering G, Gugat M, Wang K (2017)
Publication Status: Published
Publication Type: Journal article
Publication year: 2017
Journal
Publisher: AMER INST MATHEMATICAL SCIENCES-AIMS
Book Volume: 7
Pages Range: 419-448
Journal Issue: 3
DOI: 10.3934/mcrf.2017015
Abstract
For a system that is governed by the isothermal Euler equations with friction for ideal gas, the corresponding field of characteristic curves is determined by the velocity of the flow. This velocity is determined by a second-order quasilinear hyperbolic equation. For the corresponding initial-boundary value problem with Neumann-boundary feedback, we consider non-stationary solutions locally around a stationary state on a finite time interval and discuss the well-posedness of this kind of problem. We introduce a strict H-2-Lyapunov function and show that the boundary feedback constant can be chosen such that the H-2-Lyapunov function and hence also the H-2-norm of the difference between the non-stationary and the stationary state decays exponentially with time.
Authors with CRIS profile
Günter Leugering
Lehrstuhl für Angewandte Mathematik
Martin Gugat
Lehrstuhl für Angewandte Mathematik
Involved external institutions
China (CN)How to cite
APA:
Leugering, G., Gugat, M., & Wang, K. (2017). NEUMANN BOUNDARY FEEDBACK STABILIZATION FOR A NONLINEAR WAVE EQUATION: A STRICT H-2-LYAPUNOV FUNCTION. Mathematical Control and Related Fields, 7(3), 419-448. https://dx.doi.org/10.3934/mcrf.2017015
MLA:
Leugering, Günter, Martin Gugat, and Ke Wang. "NEUMANN BOUNDARY FEEDBACK STABILIZATION FOR A NONLINEAR WAVE EQUATION: A STRICT H-2-LYAPUNOV FUNCTION." Mathematical Control and Related Fields 7.3 (2017): 419-448.
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