Boundary feedback stabilization of the telegraph equation: Decay rates for vanishing damping term

Gugat M (2014)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2014

Journal

Systems & Control Letters Elsevier

Publisher: Elsevier

Book Volume: 66

Pages Range: 72-84

URI: http://ac.els-cdn.com/S0167691114000279/1-s2.0-S0167691114000279-main.pdf?_tid=631b42fa-9efc-11e3-83ef-00000aab0f26&acdnat=1393429438_c7a54e1446ab014020ff9d6d7536964a

DOI: 10.1016/j.sysconle.2014.01.007

Abstract

We study a semilinear mildly damped wave equation that contains the telegraph equation as a special case. We consider Neumann velocity boundary feedback and prove the exponential stability of the closed loop system. We show that for vanishing damping term in the partial differential equation, the decay rate of the system approaches the rate for the system governed by the wave equation without damping term. In particular, this implies that arbitrarily large decay rates can occur if the velocity damping in the partial differential equation is sufficiently small. © 2014 Elsevier B.V. All rights reserved.

Authors with CRIS profile

Martin Gugat Lehrstuhl für Angewandte Mathematik

How to cite

APA:

Gugat, M. (2014). Boundary feedback stabilization of the telegraph equation: Decay rates for vanishing damping term. Systems & Control Letters, 66, 72-84. https://dx.doi.org/10.1016/j.sysconle.2014.01.007

MLA:

Gugat, Martin. "Boundary feedback stabilization of the telegraph equation: Decay rates for vanishing damping term." Systems & Control Letters 66 (2014): 72-84.

BibTeX: Download