数学物理学报(英文版) ›› 1987, Vol. 7 ›› Issue (4): 401-409.
张秉钰, 冯德兴
Zhang Bingyu, Feng Dexing
摘要： 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.