THE EXPONENTIAL DECAY RATE OF GENERIC TREE OF 1-D WAVE EQUATIONS WITH BOUNDARY FEEDBACK CONTROLS

被引：1

作者：

Xie, Yaru ^{[1
]}

Xu, Genqi ^{[1
]}

机构：

[1] Tianjin Univ, Dept Math, Haihe Educ Pk, Tianjin 300000, MO, Peoples R China

来源：

NETWORKS AND HETEROGENEOUS MEDIA | 2016年 / 11卷 / 03期

关键词：

Wave networks; weighted energy functional; boundary feedback control; exponential decay rate; STAR-SHAPED NETWORKS; RIESZ BASIS PROPERTY; EXACT CONTROLLABILITY; HYPERBOLIC SYSTEMS; VIBRATING STRINGS; NODAL FEEDBACKS; SUPER-STABILITY; STABILIZATION; OPERATOR; SPECTRUM;

D O I：

10.3934/nhm.2016008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the exponential decay rate of generic tree of 1-d wave equations with boundary feedback controls. For the networks, there are some results on the exponential stability, but no result on estimate of the decay rate. The present work mainly estimates the decay rate for these systems, including signal wave equation, serially connected wave equations, and generic tree of 1-d wave equations. By defining the weighted energy functional of the system, and choosing suitable weighted functions, we obtain the estimation value of decay rate of the systems.

引用

页码：527 / 543

页数：17

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