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.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 2, pp. 155–166, February, 1992.
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Bazalii, B.V., Degtyarev, S.P. Stefan problem with a kinetic and the classical conditions at the free boundary. Ukr Math J 44, 139–148 (1992). https://doi.org/10.1007/BF01061735
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DOI: https://doi.org/10.1007/BF01061735