Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat Friedmann–Lemaitre–Robertson–Walker spacetimes. For the case of decelerating expansion, we show upper bounds of the lifespan of blow-up solutions by distinguishing subcritical and critical cases. Comparing to the case of the Minkowski spacetime, we discuss how the scale factor affects the lifespan of blow-up solutions of the equation.

中文翻译：

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弗里德曼-勒梅特-罗伯逊-沃克时空半线性波动方程解的爆破

考虑在空间平坦的弗里德曼-勒梅特-罗伯逊-沃克时空中具有自相互作用的无质量标量场的非线性波动方程。对于减速扩张的情况，我们通过区分亚临界和临界情况来显示爆破解决方案的寿命上限。与 Minkowski 时空的情况相比，我们讨论了比例因子如何影响方程的爆破解的寿命。