In this paper, we are concerned with the decay rate of the solution of a viscoelastic plate equation with infinite memory and logarithmic nonlinearity. We establish an explicit and general decay rate results with imposing a minimal condition on the relaxation function. In fact, we assume that the relaxation function h satisfies $$ h^{\prime}(t)\le-\xi(t) H\bigl(h(t)\bigr),\quad t\geq0, $$ where the functions ξ and H satisfy some conditions. Our proof is based on the multiplier method, convex properties, logarithmic inequalities, and some properties of integro-differential equations. Moreover, we drop the boundedness assumption on the history data, usually made in the literature. In fact, our results generalize, extend, and improve earlier results in the literature.

中文翻译：

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具有过去历史和对数非线性的粘弹性板方程的稳定性结果

在本文中，我们关注具有无限记忆和对数非线性的粘弹性板方程解的衰减率。我们通过对松弛函数施加最小条件来建立显式且通用的衰减率结果。实际上，我们假设松弛函数h满足$$ h ^ {\ prime}（t）\ le- \ xi（t）H \ bigl（h（t）\ bigr），\ quad t \ geq0，$$其中ξ和H满足某些条件。我们的证明是基于乘数法，凸性质，对数不等式和积分微分方程的某些性质。此外，我们在历史数据上删除有界假设，通常是在文献中做出的。实际上，我们的结果可以概括，扩展和改进文献中的早期结果。