Abstract
This paper is concerned with generalized Hyers-Ulam stability of the diffusion equation, partial differential & part;u(x, t)/& part;t = delta u(x, t) with u(x, 0) = f(x) for t > 0 and x is an element of R(n .)Most of the Hyers Ulam stability problems of differential equations are involved with L-infinity-norm or the supremum norm of functions with consideration of either initial conditions or forcing terms. However, an integral method of Fourier transform can be used to obtain the L-2-estimates for generalized Hyers-Ulam stability of an IVP (initial value problem) of the diffusion equation with a function f(x) as an initial condition and we will present the generalized Hyers-Ulam stability of the IVP in the sense of L-2-norm. (c) 2022 Elsevier B.V. All rights reserved.
NSTL
Elsevier