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.
Semilinear wave equation on compact Lie groups
Palmieri A.
2021-01-01
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.File in questo prodotto:
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Palmieri A. (2021 JPDOA) - Semilinear wave equation on compact Lie groups.pdf
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