Neumann boundary feedback stabilization for a nonlinear wave equation: A strict H2-Lyapunov function

Beitrag in einer Fachzeitschrift
(Originalarbeit)


Details zur Publikation

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


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 H2-Lyapunov function and show that the boundary feedback constant can be chosen such that the H2-Lyapunov function and hence also the H2-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


Zitierweisen

APA:
Gugat, M., Leugering, G., & Wang, K. (2017). Neumann boundary feedback stabilization for a nonlinear wave equation: A strict H2-Lyapunov function. Mathematical Control and Related Fields, 7(3), 419 - 448. https://dx.doi.org/10.3934/mcrf.2017015

MLA:
Gugat, Martin, Günter Leugering, and Ke Wang. "Neumann boundary feedback stabilization for a nonlinear wave equation: A strict H2-Lyapunov function." Mathematical Control and Related Fields 7.3 (2017): 419 - 448.

BibTeX: 

Zuletzt aktualisiert 2018-11-08 um 02:57