NEUMANN BOUNDARY FEEDBACK STABILIZATION FOR A NONLINEAR WAVE EQUATION: A STRICT H2LYAPUNOV FUNCTION
Journal article
Publication Details
Author(s): Leugering G, Gugat M, Wang K
Journal: → Mathematical Control and Related Fields 
Publisher: AMER INST MATHEMATICAL SCIENCESAIMS
Publication year: 2017
Volume: 7
Journal issue: 3
Pages range: 419448
ISSN: 21568472
eISSN: 21568499
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 secondorder quasilinear hyperbolic equation. For the corresponding initialboundary value problem with Neumannboundary feedback, we consider nonstationary solutions locally around a stationary state on a finite time interval and discuss the wellposedness of this kind of problem. We introduce a strict H2Lyapunov function and show that the boundary feedback constant can be chosen such that the H2Lyapunov function and hence also the H2norm of the difference between the nonstationary 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 H2LYAPUNOV FUNCTION. Mathematical Control and Related Fields, 7(3), 419448. 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 H2LYAPUNOV FUNCTION." Mathematical Control and Related Fields 7.3 (2017): 419448. 