We consider the initial boundary value problem in exterior domain for strongly damped wave equations with power-type nonlinearity \(|u|^p\). We will establish blow-up results under some conditions on the initial data and the exponent p, using the method of test function with an appropriate harmonic functions. We also study the existence of mild solution and its relation with the weak formulation.

中文翻译：

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外部域中具有强阻尼的波动方程的有限时间爆破

我们考虑具有动力型非线性\（| u | ^ p \）的强阻尼波动方程在外部域中的初始边值问题。我们将使用带有适当谐波函数的测试函数方法，在某些条件下根据初始数据和指数p建立爆破结果。我们还研究了温和溶液的存在及其与弱配方的关系。