Generalized Hyers-Ulam stability of n-dimensional wave equations in the L2-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 infinity-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.