A Stefan-Signorini problem
The paper deals with a somewhat ''non-classical'' Stefan problem of the following nature. The one-dimensional slab of ice at non-positive temperature is heated at one end, and the resulting water is immediately removed at every instant of melting. In the paper this model problem is formulated as a Stefan problem with Signorini boundary conditions at the moving boundary. Existence and uniqueness results are established for the solution of this free boundary problem, together with a certain study of regularity and of geometric features of the free boundary. Namely, the number of vertical segments of the free boundary is estimated, and the boundary itself is shown to be in \(C^{3/2}\) class.
scientific article; zbMATH DE number 3844278