On the blow – up of solutions to semilinear damped wave equations with power nonlinearity in compact Lie groups

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