Summary
The paper offers a study of a broad class of multidimensional two- phase problems of Stefan type by means of variational inequality techniques. The problems for quasilinear equations of alternatively parabolic or mixed parabolicelliptic type, mixed type nonlinear conditions at the fixed lateral boundary, involving free boundary conditions corresponding to phase transitions of both first (latent heat positive) and second kind (latent heat equal to zero) are taken into consideration. Results concerning existence of weak solutions, their uniqueness and stability are established.
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The preparation of the paper was partially carried out while the author's visiting Istituto di Analisi Numerica del C.N.R., Pavia, due to support of the C.N.R.
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Pawłow, I. A variational inequality approach to generalized two-phase Stefan problem in several space variables. Annali di Matematica pura ed applicata 131, 333–373 (1982). https://doi.org/10.1007/BF01765160
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DOI: https://doi.org/10.1007/BF01765160