Global existence for the semi-linear wave/Klein–Gordon equation associated to the harmonic oscillator in low dimensions

Global existence for the semi-linear wave/Klein–Gordon equation associated to the harmonic oscillator in low dimensions

We show that the small solution for the semi-linear wave/Klein–Gordon equation associated to the harmonic oscillator exists globally in dimension 1 and 2. Moreover, we prove that the Sobolev norm of the solution grows at most polynomially.

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Veröffentlicht in:Nonlinear differential equations and applications 2022, Vol.29 (4), Article 50
Hauptverfasser: Xue, Lingyun, Zhang, Qidi
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Harmonic oscillators
Klein-Gordon equation
Mathematics
Mathematics and Statistics
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Zusammenfassung:We show that the small solution for the semi-linear wave/Klein–Gordon equation associated to the harmonic oscillator exists globally in dimension 1 and 2. Moreover, we prove that the Sobolev norm of the solution grows at most polynomially.
ISSN:1021-9722
1420-9004
DOI:10.1007/s00030-022-00776-1