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.

Mathematics Subject Classification (2020):

• 35L05
• 93B05
• 93B07
• 35R12

Key words:

• Impulsive wave equation
• impulse control
• impulse observability
• impulse approximate controllability