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Article Dans Une Revue Journal of Functional Analysis Année : 2011

On stabilization and control for the critical Klein–Gordon equation on a 3-D compact manifold

Camille Laurent

Résumé

In this article, 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 on $\R^3$, is performed by taking care of possible geometric effects. It uses some results of S. Ibrahim on the behavior of concentrating waves on manifolds.
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Dates et versions

hal-00473592 , version 1 (15-04-2010)

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Camille Laurent. On stabilization and control for the critical Klein–Gordon equation on a 3-D compact manifold. Journal of Functional Analysis, 2011, 260 (5), pp.1304 - 1368. ⟨10.1016/j.jfa.2010.10.019⟩. ⟨hal-00473592⟩
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