General decay rates of the solution energy in a viscoelastic wave equation with boundary feedback and a nonlinear source

Islem Baaziz, Benyattou Benabderrahmane, Salah Drabla

Abstract


In a bounded domain, we consider a viscoelastic equation \[u_{tt}-\Delta u+\int_{0}^{t}g(t-\tau )\Delta u(\tau )d\tau =|u|^{\gamma }u\]
with a nonlinear feedback localized on a part of the boundary, where \(\gamma
>0\) and the relaxation function \(g\) satisfied \(g^{\prime }(t)\leq \xi
(t)g^{p}(t),\ 1\leq p<\frac{3}{2},\) and certain initial data. We establish an explicit and general decay rate result, using some properties of the convex functions. Our new results substantially improve several earlier related results in the literature.


Keywords


General decay, nonlinear source, viscoelastic, wave equation, relaxation function

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References


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DOI: http://dx.doi.org/10.24193/subbmath.2024.2.09

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