APPROXIMATION PROPERTIES OF THE PERTURBED DIFFUSION EQUATION ON THE HALF-LINE

Abstract

We prove the generalized Hyers-Ulam stability of the diffusion equation, ut(x, t)−ku_{xx}(x, t) = 0, on the half-line for a class of radially symmetric scalar functions u : (0, ∞) ×(0, ∞) → R which are twice continuously differentiable.