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Spectral controllability of some singular hyperbolic equations on networks

Fotouhi, M ; Sharif University of Technology | 2016

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  1. Type of Document: Article
  2. DOI: 10.1007/s10883-016-9330-y
  3. Publisher: Springer New York LLC , 2016
  4. Abstract:
  5. The purpose of this paper is to address the question of well-posedness and spectral controllability of the wave equation perturbed by potential on networks which may contain unbounded potentials in the external edges. It has been shown before that in the absence of any potential, there exists an optimal time T∗ (which turns out to be simply twice the sum of all length of the strings of the network) that describes the spectral controllability of the system. We will show that this holds in our case too, i.e., the potentials have no effect on the value of the optimal time T∗. The proof is based on the famous Beurling-Malliavin’s Theorem on the completeness interval of real exponentials and on a result by Redheffer who had shown that under some simple condition the completeness interval of two complex sequences are the same. © 2016 Springer Science+Business Media New York
  6. Keywords:
  7. Approximate controllability ; Network ; Spectral controllability ; Spectrum of an operator ; Complex networks ; Networks (circuits) ; Complex sequences ; Exponentials ; Hyperbolic equations ; Optimal time ; Spectrum of an operators ; Wellposedness ; Controllability
  8. Source: Journal of Dynamical and Control Systems ; 2016 , Pages 1-22 ; 10792724 (ISSN)
  9. URL: https://link.springer.com/article/10.1007%2Fs10883-016-9330-y