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2005 On basis property of a hyperbolic system with dynamic boundary condition
Bao-Zhu Guo, Gen-Qi Xu
Differential Integral Equations 18(1): 35-60 (2005).


This paper addresses the basis property of a linear hyperbolic system with dynamic boundary condition in one space variable whose general form was first studied in [15]. It is shown that under a regularity assumption, the spectrum of the system displays a distribution on the complex plane similar to zeros of a sine-type function and the generalized eigenfunctions of the system constitute a Riesz basis for its root subspace. The state space thereby decomposes into a topological direct sum of the root subspace with another invariant subspace in which the associated semigroup is supperstable: that is to say, the semigroup is identical to zero after a finite time. As a consequence, the spectrum-determined growth condition is established.


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Bao-Zhu Guo. Gen-Qi Xu. "On basis property of a hyperbolic system with dynamic boundary condition." Differential Integral Equations 18 (1) 35 - 60, 2005.


Published: 2005
First available in Project Euclid: 21 December 2012

zbMATH: 1212.93161
MathSciNet: MR2105338

Primary: 35L60
Secondary: 47D06 , 47N70 , 93C20 , 93D15

Rights: Copyright © 2005 Khayyam Publishing, Inc.


Vol.18 • No. 1 • 2005
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