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 ω and at one instant of time τ ∈ (0; T). Afterward, we study  impulse observability.