I have doubt on Stefan Problem with time boundary conditions, does this problem has an analytical solution or not? For example in the following article
Tao, L. N., The Stefan problem with arbitrary initial and boundary conditions, Q. Appl. Math. 36, 223-233 (1978). ZBL0396.76075.
They obtain some kind of analytical solution but I do not get how this is solution is different from a problem with non-time dependent boundary conditions, because actually they have an special solution with this condition