Abstract
In this paper we apply the Fourier transform to prove the Hyers-Ulam-Rassias stability for one dimensional heat equation on an infinite rod. Further, the paper investigates the stability of heat equation in with initial condition, in the sense of Hyers-Ulam-Rassias. We have also used Laplace transform to establish the modified Hyers-Ulam-Rassias stability of initial-boundary value problem for heat equation on a finite rod. Some illustrative examples are given.
Highlights
Introduction and PreliminariesThe study of stability problems for various functional equations originated from a famous talk given by Ulam in 1940
The paper investigates the stability of heat equation in n with initial condition, in the sense of Hyers-Ulam-Rassias
Ulam discussed a problem concerning the stability of homomorphisms
Summary
The study of stability problems for various functional equations originated from a famous talk given by Ulam in 1940. The results of Hyers-Ulam stability of differential equations of first order were generalized by Miura et al [13], Jung [14] and Wang et al [15]. Jung [19] proved the Hyers-Ulam stability of first-order linear partial differential equations. Lungu and Craciun [21] established results on the Ulam-Hyers stability and the generalized Ulam-HyersRassias stability of nonlinear hyperbolic partial differential equations. Definition 3 We will say that the solution of the initial value problem (1), (2) has the Hyers-Ulam-Rassias asymptotic stability with respect to 0 , if it is stable in the sense of Hyers and Ulam with respect to , and lim u x,t w x,t 0 t. Theorem 2 If u x,t C12 0,T the initial value problem (1), (2) is stable in the sense of HyersUlam-Rassias
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