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Investigation of solvability of the multidimensional two-phase Stefan and the nonstationary filtration Florin problems for second order parabolic equations in weighted Hölder spaces of functions

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Abstract

Multidimensional two-phase Stefan (k=1) and nonstationary filtration Florin (k=0) problems for second order parabolic equations in the case when the free boundary is a graph of a functionx n =Ψ k (x′t),x′∈n−1,n≥2,t∈(0,T) are studied. A unique solvability theorem in weighted Hölder spaces of functions with time power weight is proved, coercive estimates for solutions are obtained. Bibliography: 30 titles.

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Authors
  1. G. I. Bizhanova
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Dedicated to V. A. Solonnikov on his sixtieth anniversary

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 213, 1994 pp. 14–47.

Translated by N. A. Karazeeva.

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Bizhanova, G.I. Investigation of solvability of the multidimensional two-phase Stefan and the nonstationary filtration Florin problems for second order parabolic equations in weighted Hölder spaces of functions. J Math Sci 84, 823–844 (1997). https://doi.org/10.1007/BF02399935

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  • DOI: https://doi.org/10.1007/BF02399935

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