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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Global Well-Posedness and Exponential Stability Results for Bresse-Timoshenko Type Systems of Second Sound with Distributed Delay Term

Discontinuity, Nonlinearity, and Complexity 12(2) (2023) 341--363 | DOI:10.5890/DNC.2023.06.009

$^{1}$ normalsize Laboratory of pure and applied mathematics, Amar Teledji University of Laghouat, Algeria

$^{2}$ normalsize Department of Mathematics, Faculty of Sciences, University Farhat Abbas of Setif1, Algeria

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Abstract

In this paper, we consider a Bresse-Timoshenko type system of second sound with distributed delay term. Under suitable assumptions, we establish the global well-posedness of the initial and boundary value problem by using the Faedo-Galerkin approximations and some energy estimates. By using the energy method, we show exponential stability results for the system with distributed term delay acting in angular rotation, respectively. This extends earlier results in the literature.

Acknowledgments

The authors are highly grateful to the anonymous referee for his/her valuable comments and suggestions for the improvement of the paper. This research work is supported by the General Direction of Scientific Research and Technological Development (DGRSDT), Algeria.

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