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.

中文翻译：

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整个空间中粘弹性Moore-Gibson-Thompson方程的一般稳定性结果

在本文中，我们对具有II型记忆项和满足\（g ^ {\ prime}（t）\ le-\ eta（t）g（t）的松弛函数的粘弹性Moore-Gibson-Thompson方程感兴趣）\）。通过在傅立叶空间中构造适当的Lyapunov泛函，我们在\（\ left（\ beta-\ frac {\ gamma} {\ alpha}-\ frac {\ varrho} {2} \ right）> 0. \）然后给出解的L \（^ {2} \）-范数的衰减率。我们还举两个例子来说明我们的理论结果。