On stabilization and control for the critical Klein-Gordon equation on a 3-D compact manifold
Journal: Journées Équations aux dérivées partielles
Year: 2012

We study the internal stabilization and control of the critical nonlinear Klein-Gordon equation on 3-D compact manifolds. Under a geometric assumption slightly stronger than the classical geometric control condition, we prove exponential decay for some solutions bounded in the energy space but small in a lower norm. The proof combines profile decomposition and microlocal arguments. This profile decomposition, analogous to the one of Bahouri-Gérard [2] on <mml:math xmlns:mml="http://www.w3.org/19