Qualitative properties for the 1-D Impulsive Wave Equation: Controllability and Observability

Abstract

In this paper, we establish some important results for the impulsive wave equation. We begin by proving the existence of a solution. Then, we study the impulse approximate controllability where the control function acts on a subdomain $\omega$ and at one instant of time $\tau \in (0,T)$. Afterward, we study impulse observability

12 pages, 3 figures