加速扩展Friedmann-Lemaitre-Robertson-Walker时空中半线性wave equations解的爆破
Blow up of solutions of semilinear wave equations in accelerated expanding Friedmann-Lemaître-Robertson-Walker spacetime
摘要：
考虑空间平坦的Friedmann-Lemaitre-Robertson-Walker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。对于加速膨胀的情形，我们证明了具有任意次幂非线性项的方程在有限时间内爆破，并给出了爆破解的寿命的上界。与闵可夫斯基时空的情形相比，我们讨论了尺度因子对方程爆破解寿命的影响。
英文摘要：
Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat Friedmann-Lemaître-Robertson-Walker spacetimes. For the case of accelerated expansion, we show that blow-up in a finite time occurs for the equation with arbitrary power nonlinearity as well as upper bounds of the lifespan of blow-up solutions. Comparing to the case of the Minkowski spacetime, we discuss how the scale factor affects the lifespan of blow-up solutions of the equation.
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