Abstract: The convergence of the solutions of a parabolic partial differential equation on perturbed domains is considered. The domain perturbation of Sobolev spaces with time variable is first studied, and the corresponding perturbation theory of Sobolev spaces is established. Then it is shown that the solution u₈, of the equation under consideration converges to u₀ if the perturbed domain Ω₈, tends to Ω₀ in some sense as e→0.