Title: Stabilization without geometric control : a topological pressure condition
Speaker: Emmanuel Schenk
Speaker Info: Northwestern
Brief Description:
Special Note:
Abstract:
We consider the damped wave equation on a compact, negatively curved manifold (M,g) of dimension d>1 with a damping term positive and non-identically zero. In this situation, the energy decays to zero as time goes to infinity : the goal of the stabilization problem is to determine the speed of this decay. Under an hypothesis involving the negativity of a topological pressure, we obtain a spectral gap near the real axis, and an exponential decay of the energy for all initial data sufficiently regular. In particular, this result can hold in cases where the geometric control condition fails. We will give some examples, time permitting.Date: Monday, October 25, 2010