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Blow-up of solutions of semilinear wave equations in accelerated expanding Friedmann–Lemaître–Robertson–Walker spacetime

Kimitoshi Tsutaya

Graduate School of Science and Technology, Hirosaki University, Hirosaki 036-8561, Japan

E-mail Address: tsutaya@hirosaki-u.ac.jp

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and

Yuta Wakasugi

Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan

E-mail Address: wakasugi@hiroshima-u.ac.jp

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https://doi.org/10.1142/S0129055X22500039Cited by:6 (Source: Crossref)

Abstract

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 the 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.

Keywords:

AMSC: 35Q85, 35L05, 35L70

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