Boundary Control for a Generalized Wave Equation -- Revisiting Russell's Method of Control

TL;DR

This paper extends Russell's boundary control method to a generalized wave equation in nonsmooth domains with obstacles, employing scattering theory and trace theorems to establish exact controllability results.

Contribution

It introduces a novel approach for boundary control of complex wave equations in nonsmooth, multi-zone transmission domains using advanced scattering and trace techniques.

Findings

Proves exact boundary controllability in nonsmooth domains

Handles multiple transmission zones in wave equations

Utilizes scattering theory and trace theorems effectively

Abstract

In this work we study the exact boundary controllability of a generalized wave equation in a nonsmooth domain with a nontrapping obstacle. In the more general case, this work contemplates the boundary control of a transmission problem admitting several zones of transmission. The result is obtained using the technique developed by David Russell, taking advantage of the local energy decay for the problem, obtained through the Scattering Theory as used by Vodev, combined with a powerful trace Theorem due to Tataru.