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Volume 34, Issue 3
Energy Decay of Solutions to a Nondegenerate Wave Equation with a Fractional Boundary Control

Mohamed Tahri, Hanane Benkhedda & Abbes Benaissa

DOI: 10.4208/jpde.v34.n3.1

J. Part. Diff. Eq., 34 (2021), pp. 201-223.

Published online: 2021-07

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  • Abstract

In this paper, we study the energy decay rate for a one-dimensional nondegenerate wave equation under a fractional control applied at the boundary. We proved the polynomial decay result with an estimation of the decay rates. Our result is established using the frequency-domain method and Borichev-Tomilov theorem.

  • Keywords

Nondegenerate wave equation, fractional boundary control, Frequency domain method, Optimal polynomial stability.

  • AMS Subject Headings

93D15, 35B40, 47D03, 74D05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

m_tahri5@yahoo.fr (Mohamed Tahri)

benkhedda-hanane@outlook.fr (Hanane Benkhedda)

benaissa_abbes@yahoo.com (Abbes Benaissa)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-34-201, author = {Tahri , MohamedBenkhedda , Hanane and Benaissa , Abbes}, title = {Energy Decay of Solutions to a Nondegenerate Wave Equation with a Fractional Boundary Control}, journal = {Journal of Partial Differential Equations}, year = {2021}, volume = {34}, number = {3}, pages = {201--223}, abstract = {

In this paper, we study the energy decay rate for a one-dimensional nondegenerate wave equation under a fractional control applied at the boundary. We proved the polynomial decay result with an estimation of the decay rates. Our result is established using the frequency-domain method and Borichev-Tomilov theorem.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v34.n3.1}, url = {http://global-sci.org/intro/article_detail/jpde/19320.html} }
TY - JOUR T1 - Energy Decay of Solutions to a Nondegenerate Wave Equation with a Fractional Boundary Control AU - Tahri , Mohamed AU - Benkhedda , Hanane AU - Benaissa , Abbes JO - Journal of Partial Differential Equations VL - 3 SP - 201 EP - 223 PY - 2021 DA - 2021/07 SN - 34 DO - http://doi.org/10.4208/jpde.v34.n3.1 UR - https://global-sci.org/intro/article_detail/jpde/19320.html KW - Nondegenerate wave equation, fractional boundary control, Frequency domain method, Optimal polynomial stability. AB -

In this paper, we study the energy decay rate for a one-dimensional nondegenerate wave equation under a fractional control applied at the boundary. We proved the polynomial decay result with an estimation of the decay rates. Our result is established using the frequency-domain method and Borichev-Tomilov theorem.

Mohamed Tahri, Hanane Benkhedda & Abbes Benaissa. (2021). Energy Decay of Solutions to a Nondegenerate Wave Equation with a Fractional Boundary Control. Journal of Partial Differential Equations. 34 (3). 201-223. doi:10.4208/jpde.v34.n3.1
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