Geodesic
Blowup of the solution to the Cauchy problem with arbitrary positive energy for a system of Klein–Gordon equations in the de Sitter metric
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 10, pp. 1775-1779 
M. O. Korpusov; S. G. Mikhailenko. Blowup of the solution to the Cauchy problem with arbitrary positive energy for a system of Klein–Gordon equations in the de Sitter metric. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 10, pp. 1775-1779. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_10_a8/
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     title = {Blowup of the solution to the {Cauchy} problem with arbitrary positive energy for a system of {Klein{\textendash}Gordon} equations in the de {Sitter} metric},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     volume = {56},
     number = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_10_a8/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The $\phi^4$ model of a scalar (complex) field in the metric of an expanding universe, namely, in the de Sitter metric is considered. The initial energy of the system can have an arbitrarily high positive value. Sufficient conditions for solution blowup in a finite time are obtained. The existence of blowup is proved by applying H.A. Levine's modified method is used.

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