Multidimensional two-phase quasistationary Stefan problem
An analysis is being made of a two-dimensional quasi-stationary Stefan problem which is considered as a model problem for the process of crystallization of an infnite ingot moving with a constant velocity with respect to a stationary heat source. The generalized solution of the problem is sought as the limit of a sequence of solutions of the corresponding nonstationary problem when \(t \to \infty\). Existence and uniqueness of the solution are proved, and it is shown that this solution is a classical one. Then, crystallization of a plane ingot with an anisotropic structure (the heat conductivity in the \(x\)-direction is much higher than that in the \(y\)-direction) is modelled. Existence and uniqueness of the solution to the corresponding model problem are also demonstrated. Finally, it is shown that the results obtained can be carried over to three-dimensional problems.
scientific article; zbMATH DE number 492764
scientific article