Generalized Hyers–Ulam stability of  n -dimensional wave equations in the L 2 -norm

Abstract This research investigates the generalized Hyers–Ulam stability of the wave equation in an n -dimensional space, evaluated using the L 2 -norm. Typically, the results of Hyers–Ulam stability problems for differential equations are established using either the supremum norm or L ∞ -norm, with a focus on initial conditions or forcing terms to estimate error terms. In this study, we employ an integral approach utilizing the Fourier transform and Parseval’s equality to derive the L 2 -bound for the generalized Hyers–Ulam stability of the governing equation, specifically within the framework of the L 2 -norm. Furthermore, to validate the analytical estimates, we conduct numerical experiments incorporating various types of control functions based on the obtained results.