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

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. s(A) = sup{ λ, λ ∈ σ(A)}.