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Stabilization of a coupled wave equations with one localized non-regular fractional Kelvin-Voigt damping with non-smooth coefficients
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  • Li Zhang,
  • Wenjun Liu,
  • Yanning An,
  • Xinxin Cao
Li Zhang
Nanjing University of Information Science and Technology

Corresponding Author:[email protected]

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Wenjun Liu
Nanjing University of Information Science and Technology
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Yanning An
Nanjing University of Information Science and Technology
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Xinxin Cao
Nanjing University of Information Science and Technology
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Abstract

In this paper, we study the stabilization of a coupled wave system formed by one localized non-regular fractional viscoelastic damping of Kelvin-Voigt type and localized non-smooth coefficients. Our main aim is to prove that the C0-semigroup associated with this model is strong stability and decays polynomially at a rate of t−1. By introducing a new system to deal with fractional Kelvin-Voigt damping, we obtain a new equivalent augmented system, so as to show the well-posedness of the system based on Lumer-Phillips theorem. We achieve the strong stability for the C0-semigroup associated with this new model by using a general criteria of Arendt-Batty, and then turn out a polynomial energy decay rate of order t−1 with the help of a frequency domain approach.
17 Mar 2022Submitted to Mathematical Methods in the Applied Sciences
18 Mar 2022Submission Checks Completed
18 Mar 2022Assigned to Editor
25 Mar 2022Reviewer(s) Assigned
07 Jun 2022Review(s) Completed, Editorial Evaluation Pending
07 Jun 2022Editorial Decision: Revise Major
05 Jul 20221st Revision Received
07 Jul 2022Submission Checks Completed
07 Jul 2022Assigned to Editor
22 Aug 2022Reviewer(s) Assigned
14 Oct 2022Review(s) Completed, Editorial Evaluation Pending
17 Oct 2022Editorial Decision: Revise Major
13 Nov 20222nd Revision Received
14 Nov 2022Submission Checks Completed
14 Nov 2022Assigned to Editor
14 Nov 2022Review(s) Completed, Editorial Evaluation Pending
12 Dec 2022Reviewer(s) Assigned
02 Jan 2023Editorial Decision: Accept