In this paper, we study weakly coupled systems for semilinear wave equations with distinct nonlinear memory terms in general forms, and the corresponding single semilinear equation with general nonlinear memory terms. Thanks to fixed point theory, we prove local (in time) existence of solutions with the $L^1$ assumption on the memory kernels. Then, blow-up results for energy solutions are derived by applying iteration methods associated with slicing procedure. We investigate interactions on the blow-up conditions under different decreasing assumptions on the memory term. Particularly, a new threshold for the kernels on interplay effect is found. Additionally, we give some applications of our results on semilinear wave equations and acoustic wave equations.

在本文中，我们研究一般形式的具有明显非线性记忆项的半线性波动方程的弱耦合系统，以及具有一般非线性记忆项的相应单个半线性方程的弱耦合系统。多亏了定点理论，我们证明了解的局部（及时）存在。${\mathrm{大号}}^{\mathrm{1个}}$关于内存内核的假设。然后，通过应用与切片过程相关的迭代方法，得出能量解决方案的爆炸结果。我们研究在记忆条件下不同递减假设下爆炸条件下的相互作用。特别是，发现了内核之间相互作用影响的新阈值。此外，我们将结果应用于半线性波动方程和声波方程。