Waves, damped wave and observation

TL;DR

This paper studies wave equations in bounded domains, exploring inequalities related to trapped rays, their impact on control theory, and methods for designing approximate control functions using iterative time reversal.

Contribution

It links inequalities for trapped rays with damped wave decay rates and introduces an iterative time reversal method for approximate control design.

Findings

Established inequalities for trapped rays in wave equations.

Connected these inequalities to decay rates of damped wave equations.

Proposed an iterative time reversal method for control function design.

Abstract

We consider the wave equation in a bounded domain (eventually convex). Two kinds of inequality are described when occurs trapped ray. Applications to control theory are given. First, we link such kind of estimate with the damped wave equation and its decay rate. Next, we describe the design of an approximate control function by an iterative time reversal method.