An elliptic-parabolic free boundary problem: continuity of the interface
Jan H. Hulshof · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1987
Synopsis In this paper we establish continuity of the interface of the weak solution to an elliptic-parabolic problem. The physical background is the theory of partially saturated fluid flows in porous media. Our method is based on the maximum principle for parabolic equations. An essential assumption is that the flow is one-dimensional.