The current paper deals with the proof of a global solution of a viscoelasticity singular one-dimensional system with localized frictional damping and general source terms, taking into consideration nonlocal boundary condition. Moreover, similar to that in Boulaaras’ recent studies by constructing a Lyapunov functional and use it together with the perturbed energy method in order to prove a general decay result.

中文翻译：

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具有奇异源和局部摩擦阻尼项的两个奇异非线性粘弹性方程组的整体存在与衰减

本文考虑了非局部边界条件，提出了具有局部摩擦阻尼和广义源项的粘弹性奇异一维系统的整体解的证明。此外，类似于Boulaaras最近的研究，通过构造Lyapunov泛函并将其与微分能量法一起使用，以证明一般的衰变结果。