This article is cited in 2 papers

Blowup of the solution to the Cauchy problem with arbitrary positive energy for a system of Klein–Gordon equations in the de Sitter metric

M. O. Korpusov, S. G. Mikhailenko

Faculty of Physics, Moscow State University, Moscow, Russia

Abstract: 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.

Key words: finite-time blowup, generalized Klein–Gordon equations, nonlinear hyperbolic equations, nonlinear mixed boundary value problems, field theory.

UDC: 517.957

Received: 14.12.2015

DOI: 10.7868/S0044466916100124

 English version: Computational Mathematics and Mathematical Physics, 2016, 56:10, 1758–1762

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