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

Yaru Xie | Zendy; Genqi Xu | Zendy

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

Author(s) -

Yaru Xie,

Genqi Xu

Publication year - 2016

Publication title -

networks and heterogeneous media

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 34

eISSN - 1556-181X

pISSN - 1556-1801

DOI - 10.3934/nhm.2016008

Subject(s) - exponential decay , wave equation , exponential function , exponential growth , exponential stability , work (physics) , tree (set theory) , mathematical analysis , physics , energy (signal processing) , mathematics , boundary value problem , quantum mechanics , nonlinear system

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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