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 commentarXiv admin note: substantial text overlap with arXiv:2005.13479

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• 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