Semilinear wave equation on compact Lie groups

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.

arXiv admin note: substantial text overlap with arXiv:2005.13479

References in corpus (3)

• Fundamental Solutions for the Klein-Gordon Equation in de Sitter Spacetime
• Blow-up results for semilinear damped wave equations in Einstein-de Sitter spacetime
• On the blow-up of solutions to semilinear damped wave equations with power nonlinearity in compact Lie groups

Cited by in corpus (3)

• A global existence result for a semilinear wave equation with lower order terms on compact Lie groups
• Heat and wave type equations with non-local operators, I. Compact Lie groups
• Estimates for the nonlinear viscoelastic damped wave equation on compact Lie groups