Research Article

Qualitative properties for the 1 − D impulsive wave equation: controllability and observability

Published in: Quaestiones Mathematicae
Volume 45 , issue 8 , 2022 , pages: 1229–1241

DOI: 10.2989/16073606.2021.1940346

Author(s): Akram Ben Aissa , Tunisia , Walid Zouhair , Morocco

Keywords: 35L05 , 93B05 , 93B07 , 35R12 , 35L05 , 93B05 , 93B07 , 35R12

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.

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