The paper studies a system of nonlinear viscoelastic Kirchhoff system with a time varying delay and general coupling terms. We prove the global existence of solutions in a bounded domain using the energy and Faedo–Galerkin methods with respect to the condition on the parameters in the coupling terms together with the weight condition as regards the delay terms in the feedback and the delay speed. Furthermore, we construct some convex function properties, and we prove the uniform stability estimate.

中文翻译：

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具有时变时滞的广义耦合非退化Kirchhoff系统解的整体存在和指数衰减

本文研究了具有时变时滞和广义耦合项的非线性粘弹性基尔霍夫系统。我们使用能量和Faedo-Galerkin方法针对耦合项中参数的条件以及权重条件（关于反馈中的延迟项和延迟速度）证明了有界域中解的整体存在性。此外，我们构造了一些凸函数性质，并证明了一致的稳定性估计。