Abstract
In this note, we prove a blow-up result for the semilinear damped wave equation in a compact Lie group with power nonlinearity |u|p for any p>1, under suitable integral sign assumptions for the initial data, by using an iteration argument. A byproduct of this method is the upper bound estimate for the lifespan of a local in time solution. As a preliminary result, a local (in time) existence result is proved in the energy space via Fourier analysis on compact Lie groups.
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