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
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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.
@article{ZVMMF_2016_56_10_a8,
author = {M. O. Korpusov and S. G. Mikhailenko},
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},
pages = {1775--1779},
publisher = {mathdoc},
volume = {56},
number = {10},
year = {2016},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_10_a8/}
}
TY - JOUR AU - M. O. Korpusov AU - S. G. Mikhailenko TI - Blowup of the solution to the Cauchy problem with arbitrary positive energy for a system of Klein–Gordon equations in the de Sitter metric JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2016 SP - 1775 EP - 1779 VL - 56 IS - 10 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_10_a8/ LA - ru ID - ZVMMF_2016_56_10_a8 ER -
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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/