Stefan problem with a kinetic and the classical conditions at the free boundary

Abstract

The Stefan problem is considered with the kinetic condition u+=u−=ɛk(y, τ)-ɛv at the phase interface, where k(y, τ) is the half-sum of the principal curvatures of the free boundary and v is the speed of its shifting in the direction of a normal. The solvability of a modified Stefan problem in spaces of smooth functions and the convergence of its solutions as ɛ→0 to a solution of the classical Stefan problem are proved.