We consider a coupled system of viscoelastic wave equation with weak, strong damping and power nonlinearity. For a single viscoelastic wave equation, we have already obtained a global solution, its decay rate and finite‐time blow‐up [1]. In this paper, we extend these results to a coupled system. First, we obtain a global solution and derive its decay rate by a decreasing energy. Finally, we apply the concavity method in order to show that the solution blows up in finite time under nonclassic constraint on kernel functions.

中文翻译：

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具有可变指数的非线性阻尼波方程的耦合系统动力学。

我们考虑具有弱，强阻尼和功率非线性的粘弹性波动方程的耦合系统。对于单个粘弹性波动方程，我们已经获得了一个整体解，其衰减率和有限时间爆炸[1]。在本文中，我们将这些结果扩展到耦合系统。首先，我们获得一个整体解，并通过减少能量来推导其衰减率。最后，我们使用凹度法来证明在非经典约束下对核函数的求解在有限的时间内爆炸。