Blow up of solutions of semilinear wave equations related to nonlinear waves in de Sitter spacetime

Kimitoshi Tsutaya () and Yuta Wakasugi ()
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Kimitoshi Tsutaya: Hirosaki University
Yuta Wakasugi: Hiroshima University

Partial Differential Equations and Applications, 2022, vol. 3, issue 1, 1-10

Abstract: Abstract 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.

Keywords: Wave equation; Blow-up; Lifespan; de Sitter spacetime; 35Q85; 35L05; 35L70 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s42985-021-00145-0

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