# American Institute of Mathematical Sciences

September  2016, 11(3): 527-543. doi: 10.3934/nhm.2016008

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

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

Received  October 2014 Revised  February 2016 Published  August 2016

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.
Citation: Yaru Xie, Genqi Xu. The exponential decay rate of generic tree of 1-d wave equations with boundary feedback controls. Networks & Heterogeneous Media, 2016, 11 (3) : 527-543. doi: 10.3934/nhm.2016008
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