Differential and Integral Equations

On basis property of a hyperbolic system with dynamic boundary condition

Bao-Zhu Guo and Gen-Qi Xu

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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.

Article information

Differential Integral Equations, Volume 18, Number 1 (2005), 35-60.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35L60: Nonlinear first-order hyperbolic equations
Secondary: 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 47N70: Applications in systems theory, circuits, and control theory 93C20: Systems governed by partial differential equations 93D15: Stabilization of systems by feedback


Guo, Bao-Zhu; Xu, Gen-Qi. On basis property of a hyperbolic system with dynamic boundary condition. Differential Integral Equations 18 (2005), no. 1, 35--60. https://projecteuclid.org/euclid.die/1356060235

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