NEUMANN BOUNDARY FEEDBACK STABILIZATION FOR A NONLINEAR WAVE EQUATION: A STRICT H-2-LYAPUNOV FUNCTION

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autorinnen und Autoren: Leugering G, Gugat M, Wang K
Zeitschrift: Mathematical Control and Related Fields
Verlag: AMER INST MATHEMATICAL SCIENCES-AIMS
Jahr der Veröffentlichung: 2017
Band: 7
Heftnummer: 3
Seitenbereich: 419-448
ISSN: 2156-8472
eISSN: 2156-8499


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.



FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Gugat, Martin apl. Prof. Dr.
Lehrstuhl für Angewandte Mathematik
Leugering, Günter Prof. Dr.
Lehrstuhl für Angewandte Mathematik


Einrichtungen weiterer Autorinnen und Autoren

Fudan University / 复旦大学


Zitierweisen

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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Zuletzt aktualisiert 2018-06-08 um 11:19