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

Journal article


Publication Details

Author(s): Leugering G, Gugat M, Wang K
Journal: Mathematical Control and Related Fields
Publisher: AMER INST MATHEMATICAL SCIENCES-AIMS
Publication year: 2017
Volume: 7
Journal issue: 3
Pages range: 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 Authors / FAU Editors

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


External institutions
Fudan University / 复旦大学


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.

BibTeX: 

Last updated on 2018-06-08 at 11:19