Stefan problem with a kinetic and the classical conditions at the free boundary
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.
English version (Springer): Ukrainian Mathematical Journal 44 (1992), no. 2, pp 139-148.
Citation Example: Bazalii B. V., Degtyarev S. P. Stefan problem with a kinetic and the classical conditions at the free boundary // Ukr. Mat. Zh. - 1992. - 44, № 2. - pp. 155–166.