Abstract
In this note, we study the semilinear wave equation with power nonlinearity \(|u|^p\) on compact Lie groups. First, we prove a local in time existence result in the energy space via Fourier analysis on compact Lie groups. Then, we prove a blow-up result for the semilinear Cauchy problem for any \(p>1\), under suitable sign assumptions for the initial data. Furthermore, sharp lifespan estimates for local (in time) solutions are derived.
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Palmieri, A. Semilinear wave equation on compact Lie groups. J. Pseudo-Differ. Oper. Appl. 12, 43 (2021). https://doi.org/10.1007/s11868-021-00414-x
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DOI: https://doi.org/10.1007/s11868-021-00414-x