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

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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Cited by in corpus (5)

• On the critical exponent and sharp lifespan estimates for semilinear damped wave equations with data from Sobolev spaces of negative order
• A note on blow-up results for semilinear wave equations in de Sitter and anti-de Sitter spacetimes
• Semilinear wave equation on compact Lie groups
• A global existence result for a semilinear wave equation with lower order terms on compact Lie groups
• Estimates for the nonlinear viscoelastic damped wave equation on compact Lie groups