A Harmonic Analysis Proof of the Boundary Observability Inequality for the Wave Equation and Visco-Elastic Equation

TL;DR

This paper provides an elementary harmonic analysis proof of the boundary observability inequality for wave and visco-elastic equations, offering explicit constants and extending the method to more complex models.

Contribution

It introduces a simple harmonic analysis approach to establish boundary observability inequalities for wave and visco-elastic equations, with explicit constants and broader applicability.

Findings

Elementary harmonic analysis proof for wave equation observability

Extension of the method to visco-elastic wave equations

Explicit constant in the observability inequality

Abstract

In this paper, we give a harmonic analysis proof of the Neumann boundary observability inequality for the wave equation in an arbitrary space dimension. Our proof is elementary in nature and gives a simple, explicit constant. We also extend the method to prove the observability inequality of a visco-elastic wave equation.