Seminar | March 13 | 2:10-3 p.m. | 732 Evans Hall
Long Jin, Purdue University
In this talk, we discuss some recent results concerning the control and stabilization on a compact hyperbolic surface. In particular, we show that
the Laplace eigenfunctions have uniform lower bounds on any nonempty open set;
the linear Schrödinger equation is exactly controllable by any nonempty open set; and
the energy of solutions to the linear damped wave equation with regular initial data decay exponentially for any smooth damping function.
The new ingredient is the fractal uncertainty principle for porous sets by Bourgain–Dyatlov. This is partially based on joint work with Semyon Dyatlov.