In this paper, the blow-up of solutions to the Cauchy problems for semilinear Moore–Gibson–Thompson equations with power nonlinearity $|u{|}^p$, derivative nonlinearity $|u_t{|}^p$, combined nonlinearity $|u_t{|}^p+|u{|}^q$ are investigated. Upper bound lifespan estimates of solutions to the problems in the sub-critical and critical cases are also deduced by applying the test function approach. It is worth noticing that blow-up results are valid in the conservative case. The main novelty is that the critical exponents in our cases are associated with the well-known Strauss exponent and Glassey exponent.

中文翻译：

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半线性Moore–Gibson–Thompson方程解的爆破和寿命估计

在本文中，幂非线性的半线性Moore–Gibson–Thompson方程的Cauchy问题解的爆炸式增长 $|ü{|}^p$，导数非线性 $|{ü}_{Ť}{|}^p$，组合非线性 $|{ü}_{Ť}{|}^p+|ü{|}^q$被调查。通过应用测试函数方法，还可以得出亚临界和关键情况下问题的解决方案的上限寿命估计。值得注意的是，在保守的情况下，爆破结果是有效的。主要的新颖之处在于，在我们的案例中，关键指数与著名的Strauss指数和Glassey指数相关。