2014
DOI: 10.2298/fil1405073p
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On the existence of global solutions for a nonlinear Klein-Gordon equation

Abstract: The aim of this work is to study the global existence of solutions for the Cauchy problem of a Klein-Gordon equation with high energy initial data. The proof relies on constructing a new functional, which includes both the initial displacement and the initial velocity: with sign preserving property of the new functional we show the existence of global weak solutions.

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Cited by 8 publications
(1 citation statement)
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References 26 publications
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“…By this, the exponential decay rate of the global solutions was proved. Polat and Taskesen [16] also investigated the existence of solutions globally for equation (1), where α = 0, β = 1 by using the potential well method. Moreover, asymptotic behavior of global solutions was obtained by Xu [19].…”
Section: Introductionmentioning
confidence: 99%
“…By this, the exponential decay rate of the global solutions was proved. Polat and Taskesen [16] also investigated the existence of solutions globally for equation (1), where α = 0, β = 1 by using the potential well method. Moreover, asymptotic behavior of global solutions was obtained by Xu [19].…”
Section: Introductionmentioning
confidence: 99%