Analysis Seminar: "Harmonic Analysis Proof of the Boundary Observability Inequality for the Wave Equation"

Abstract:  The exact boundary controllability for the wave equation (or other type of hyperbolic equations) is a well-studied subject with an extensive body of literature behind. The typical method is to use the duality and transfer the controllability for the wave equation into the observability question of the dual problem. Standard ways to prove the observability inequality use microlocal analysis techniques and Carleman estimates. The harmonic analysis approach (or so called moment problem method) was also used in the past but was only successful when the space dimension of the problem is equal to 1. In this talk I will present a new harmonic analysis proof of the Neumann boundary observability inequality for the wave equation which works in arbitrary space dimension. The advantages of this approach are the simplicity of the constant and the elementary nature of the entire proof. This is joint work with A. W. Green and S. Liu.

Host: Brett Wick