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arXiv · 2103.01219

Blow up of solutions of semilinear wave equations in accelerated expanding Friedmann-Lema\^{i}tre-Robertson-Walker spacetime

Kimitoshi Tsutaya·Yuta Wakasugi
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Abstract

Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat Friedmann-Lema\^{i}tre-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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Kimitoshi Tsutaya, Yuta Wakasugi. 2021-02-27. Blow up of solutions of semilinear wave equations in accelerated expanding Friedmann-Lema\^{i}tre-Robertson-Walker spacetime. https://doi.org/10.1142/s0129055x22500039

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