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Article Dans Une Revue American Journal of Mathematics Année : 2014

Carleman estimates for the Zaremba Boundary Condition and Stabilization of Waves

Pierre Cornilleau
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Luc Robbiano

Résumé

In this paper, we shall prove a Carleman estimate for the so-called Zaremba problem. Using some techniques of interpolation and spectral estimates, we deduce a result of stabilization for the wave equation by means of a linear Neumann feedback on the boundary. This extends previous results from the literature: indeed, our logarithmic decay result is obtained while the part where the feedback is applied contacts the boundary zone driven by an homogeneous Dirichlet condition. We also derive a controllability result for the heat equation with the Zaremba boundary condition.
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Dates et versions

hal-00634867 , version 1 (24-10-2011)
hal-00634867 , version 2 (31-07-2012)

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Pierre Cornilleau, Luc Robbiano. Carleman estimates for the Zaremba Boundary Condition and Stabilization of Waves. American Journal of Mathematics, 2014, 136, pp.393-444. ⟨10.1353/ajm.2014.0014⟩. ⟨hal-00634867v2⟩
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