This paper considers a one-dimensional porous system damped with weakly nonlinear feedback in the presence of a nonlinear delay. We prove the global existence and uniqueness results using the Faedo–Galerkin procedure. Furthermore, under appropriate assumptions on the weight of the delay and without imposing any restrictive growth assumption on the damping term at the origin, we establish an energy decay rate, using a perturbed energy method and some properties of convex functions in case of the same speed of propagation in the two equations of the system.

中文翻译：

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具有非线性延迟的弱非线性阻尼多孔系统的能量衰减

本文考虑在存在非线性延迟的情况下用弱非线性反馈阻尼的一维多孔系统。我们使用 Faedo-Galerkin 过程证明了全局存在性和唯一性结果。此外，在对延迟权重的适当假设下，并且不对原点处的阻尼项施加任何限制性增长假设，我们使用摄动能量方法和凸函数的一些性质在相同速度的情况下建立能量衰减率在系统的两个方程中的传播。