The exponential decay rate of generic tree of 1-d wave equations with boundary feedback controls

Yaru  Xie; Genqi  Xu

doi:10.3934/nhm.2016008

Article Contents

2016, Volume 11, Issue 3: 527-543. Doi: 10.3934/nhm.2016008

This issue Previous Article Evolution of spoon-shaped networks Next Article

The exponential decay rate of generic tree of 1-d wave equations with boundary feedback controls

Yaru Xie^1, and
Genqi Xu^1,

1.
Department of Mathematics, Tianjin University, Haihe Education Park, Tianjin, Tianjin, MO 300000

Received: September 30, 2014

Revised: January 31, 2016

Published: August 2016

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Abstract

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.

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Mathematics Subject Classification: Primary: 35L05, 37L45; Secondary: 37L15, 90B10.

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