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Lifespan of solutions to wave equations in de Sitter spacetime

Part of: Dynamical problems Hyperbolic equations and systems

Published online by Cambridge University Press:  10 April 2018

Weiping Yan
Weiping Yan*
Affiliation:
School of Mathematics, Xiamen University, Xiamen 361000, People's Republic of China (yanwp@xmu.edu.cn)
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Abstract

We consider the finite-time blow-up of solutions for the following two kinds of nonlinear wave equation in de Sitter spacetime:

This proof is based on a new blow-up criterion, which generalizes that by Sideris. Furthermore, we give the lifespan estimate of solutions for the problems.

Keywords

blow-upwave equationlifespan

MSC classification

Primary: 35L05: Wave equation 74H35: Singularities, blowup, stress concentrations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 6 , December 2018 , pp. 1313 - 1330
Copyright
Copyright © Royal Society of Edinburgh 2018 

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