Energy decay for the damped wave equation under a pressure condition

Emmanuel Schenck (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

We establish the presence of a spectral gap near the real axis for the damped wave equation on a manifold with negative curvature. This results holds under a dynamical condition expressed by the negativity of a topological pressure with respect to the geodesic flow. As an application, we show an exponential decay of the energy for all initial data sufficiently regular. This decay is governed by the imaginary part of a finite number of eigenvalues close to the real axis.

Mots clés: stabilization; damped wave equation; Anosov flows

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Emmanuel Schenck. Energy decay for the damped wave equation under a pressure condition. 2009. ⟨hal-00415529⟩