Blow up of solutions of semilinear wave equations related to nonlinear waves in de Sitter spacetime
Blow up of solutions of semilinear wave equations related to nonlinear waves in de Sitter spacetime
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DOI：
10.1007/s42985-021-00145-0
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发表时间：
2021-12
期刊：
影响因子：
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通讯作者：
K. Tsutaya;Yuta Wakasugi
中科院分区：
文献类型：
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作者：
K. Tsutaya;Yuta Wakasugi
考虑空间平坦的德西特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。我们证明，具有任意幂非线性以及爆炸解寿命上限的方程会在有限时间内发生爆炸。爆炸条件与加速膨胀的弗里德曼-勒梅特-罗伯逊-沃克 (FLRW) 时空相同。我们还对空间导数非线性项显示了相同的结果。
Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat de Sitter spacetime. 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. The blow-up condition is the same as in the accelerated expanding Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. We also show the same results for the space derivative nonlinear term.