Boundary controllability of two coupled wave equations with space-time first-order coupling in 1-D

TL;DR

This paper investigates the exact controllability of two coupled 1-D wave equations with space-time dependent first-order coupling, providing necessary and sufficient conditions for high-frequency controllability and unique continuation in cascade configurations.

Contribution

It establishes precise controllability criteria for coupled wave equations with variable coefficients, advancing understanding of control in complex PDE systems.

Findings

Necessary and sufficient conditions for high-frequency controllability.

Unique continuation results for cascade coupled wave equations.

Analysis of controllability with space-time dependent coefficients.

Abstract

This paper is devoted to study exact controllability of two one-dimensional coupled wave equations with first-order coupling terms with coefficients depending on space and time. We give a necessary and sufficient condition for both exact controllability in high frequency in the general case and the unique continuation in the cascade case.