Abstract
In this paper, we are interested in a viscoelastic Moore–Gibson–Thompson equation with a type-II memory term and a relaxation function satisfying \(g^{\prime }(t)\le -\eta (t)g(t)\). By constructing appropriate Lyapunov functionals in the Fourier space, we establish a general decay estimate of the solution under the condition \(\left( \beta -\frac{\gamma }{\alpha }-\frac{\varrho }{2}\right) >0.\) We then give the decay rate of the L\(^{2}\)-norm of the solution. We also give two examples to illustrate our theoretical results.
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Acknowledgements
The authors thank an anonymous referee for his/her careful reading and valuable comments and the university Ferhat Abbas, Setif 1 and University of Sharjah. The second author is sponsored by the University of Sharjah, Research group MASEP. This work was initiated during the visit of the first author to the University of Sharjah.
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Bounadja, H., Messaoudi, S. A General Stability Result for a Viscoelastic Moore–Gibson–Thompson Equation in the Whole Space. Appl Math Optim 84 (Suppl 1), 509–521 (2021). https://doi.org/10.1007/s00245-021-09777-5
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DOI: https://doi.org/10.1007/s00245-021-09777-5