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

被引：17

作者：

Gugat, Martin ^{[1
]}

机构：

[1] Univ Erlangen Nurnberg, Dept Math, D-91058 Erlangen, Germany

来源：

SYSTEMS & CONTROL LETTERS | 2014年 / 66卷

关键词：

Boundary feedback; Hyperbolic partial differential equation; Exponential stability; Decay rate; Telegraph equation; Nonlinear wave equation; Damping; Anti-damping; Semilinear wave equation; EXPONENTIAL DECAY; WAVE-EQUATION;

D O I：

10.1016/j.sysconle.2014.01.007

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：72 / 84

页数：13

共 14 条

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