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Oblique projection local feedback stabilization of nonautonomous semilinear damped wave-like equations

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2020

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Rodrigues, Sérgio S.

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https://doi.org/10.1016/j.jde.2020.04.033
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Journal of Differential Equations. Elsevier. 2020, 269(7), pp. 6163-6192. ISSN 0022-0396. eISSN 1090-2732. Available under: doi: 10.1016/j.jde.2020.04.033

Zusammenfassung

The stabilization of a class of nonlinear weakly damped wave equations by means of a finite-dimensional feedback control is investigated. The stabilizing control is constructed based on an appropriate oblique projection and it enters as a time-dependent linear combination of a finite number of suitable indicator functions supported in small regions. Firstly, it is shown that an oblique projection feedback is able to globally exponentially stabilize linear nonautonomous weakly damped wave equations. Then, relying on this result, the local stabilization for semilinear equations is proven for a suitable class of nonlinearities. Finally, numerical experiments are given which validate the theoretical results.

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Fachgebiet (DDC)
510 Mathematik

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Exponential stabilization, Nonautonomous wave systems, Finite-dimensional controller, Oblique projection feedback

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ISO 690AZMI, Behzad, Sérgio S. RODRIGUES, 2020. Oblique projection local feedback stabilization of nonautonomous semilinear damped wave-like equations. In: Journal of Differential Equations. Elsevier. 2020, 269(7), pp. 6163-6192. ISSN 0022-0396. eISSN 1090-2732. Available under: doi: 10.1016/j.jde.2020.04.033
BibTex
@article{Azmi2020Obliq-56296,
  year={2020},
  doi={10.1016/j.jde.2020.04.033},
  title={Oblique projection local feedback stabilization of nonautonomous semilinear damped wave-like equations},
  number={7},
  volume={269},
  issn={0022-0396},
  journal={Journal of Differential Equations},
  pages={6163--6192},
  author={Azmi, Behzad and Rodrigues, Sérgio S.}
}
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