In this paper we consider the blow-up of solutions to a weakly coupled system of semilinear damped wave equations in the scattering case with nonlinearities of mixed type. The proof of the blow-up results is based on an iteration argument. We find as critical curve for the pair of exponents (p, q) in the nonlinear terms the same one found for the weakly coupled system of semilinear wave equations with the same kind of nonlinearities. In the critical and not-damped case we combine an iteration argument with the so-called slicing method to show the blow-up dynamic of a weighted version of the functionals used in the subcritical case.

中文翻译：

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具有混合非线性项的散射情况下半线性阻尼波动方程的弱耦合系统整体解的不存在。

在本文中，我们考虑了在具有混合非线性的散射情况下，半线性阻尼波方程的弱耦合系统解的爆破。爆破结果的证明是基于迭代参数的。我们发现，在非线性项中，一对指数（p，  q）的临界曲线与在具有相同非线性的半线性波动方程的弱耦合系统中发现的相同。在临界和非阻尼情况下，我们将迭代参数与所谓的切片方法结合起来，以显示在亚临界情况下使用的功能的加权版本的爆炸动态。