This article considers a dynamical system with delay described by a differential equation with partial derivatives of hyperbolic type and delay with respect to a time variable. We establish in Theorem 3.1 the k(t)-stability of weak solution under suitable initial conditions in \(\mathbb{R}^n, n>4\) by introducing appropriate Lyapunov functions.

中文翻译：

---

$ \ mathbb {R} ^ n $中具时变时滞和弱粘弹性的平板方程解的稳定性

本文考虑具有时滞的动力系统，该时滞由一个微分方程描述，该系统具有双曲型偏导数和相对于时间变量的时滞。通过引入适当的Lyapunov函数，在定理3.1中建立了在（\ mathbb {R} ^ n，n> 4 \）中适当初始条件下的弱解的k（t）稳定性。