JUSTIFICATION OF A QUASISTATIONARY APPROXIMATION FOR THE STEFAN PROBLEM

摘要

Unique solvability of the one-phase Stefan problem with a small multiplier e at the time derivative in the equation is proved on a certain time interval independent of ε for ε ∈ (0, ε_0). The solution to the Stefan problem is compared with the solution to the Hele-Show problem,, which describes the process of melting materials with zero specifie heat ε and can be regarded as a quasistationary approximation for the Stefan problem. It is shown that the difference of the solutions has order O(ε) + O(e~(-(ct)/ε)). This provides a justification of the quasistationary approximation.