In this paper, we consider a coupled system of two biharmonic equations with damping and source terms of variable-exponent nonlinearities, supplemented with initial and mixed boundary conditions. We establish an existence and uniqueness result of a weak solution, under suitable assumptions on the variable exponents. Then, we show that solutions with negative-initial energy blow up in finite time. To illustrate our theoritical findings, we present two numerical examples.

中文翻译：

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具有非标准非线性的双调和耦合系统：存在性、爆炸性和数值

在本文中，我们考虑两个双调和方程的耦合系统，其具有阻尼和变指数非线性源项，并补充初始和混合边界条件。在变量指数的适当假设下，我们建立了弱解的存在性和唯一性结果。然后，我们证明具有负初始能量的解会在有限时间内爆炸。为了说明我们的理论发现，我们提出了两个数值例子。