MULTIDIMENSIONAL 2-PHASE QUASI-STATIONARY STEFAN PROBLEM

Existence and uniqueness of the classic solution to a two-dimensional quasistationary Stefan problem are considered. The family of model problems dependent on the parameter epsilon > 0 which defines a heat conductivity of a matter in the direction of the x-axis is analysed. When epsilon --> 0 it is approximated by the approximate model problem having less dimensions. Analogous results are also valid for a three-dimensional problem.