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

Gugat M, Leugering G, Wang K (2017)


Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2017

Journal

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 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.

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How to cite

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.

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