A global existence result for a semilinear wave equation with lower order terms on compact Lie groups

Abstract

In this paper, we study the semilinear wave equation with lower order terms (damping and mass) and with power type nonlinearity $|u{|}^p$ on compact Lie groups. We will prove the global in time existence of small data solutions in the evolution energy space without requiring any lower bounds for $p>1$. In our approach, we employ some results from Fourier analysis on compact Lie groups.

arXiv admin note: text overlap with arXiv:2005.13479, arXiv:2005.14543

References in corpus (4)

• Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity
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Cited by in corpus (2)

• On the blow-up of solutions to semilinear damped wave equations with power nonlinearity in compact Lie groups
• Estimates for the nonlinear viscoelastic damped wave equation on compact Lie groups