Controllability conditions and non-concentration phenomena for the heat and wave equations
- Marc Rouveyrol (Université Paris-Saclay)
Abstract
The controllability problem for a given partial differential equation (PDE) consists in sending any initial condition to zero with a right-hand-side active only in a given subregion
First, I will explain how controllability of the heat equation is implied by so-called spectral estimates for frequency-localized functions. These spectral estimates are themselves equivalent to an equidistribution property of
I will then talk about a similar problem for the damped wave equation. In that case, concentration of waves along geodesics of the manifold must be avoided to achieve controllability. When the damping is continuous, the Geometric Control Condition (GCC) gives a sharp condition on the control set