We investigate the one-phase Florin problem for a parabolic equation with nonlocal condition. Theorems on the existence and uniqueness of a solution are proved, and a priori estimates for the solution are obtained.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 1, pp. 71–80, January, 2012.
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Takhirov, Z.O., Turaev, R.N. Problem with nonlocal condition on the free boundary. Ukr Math J 64, 78–88 (2012). https://doi.org/10.1007/s11253-012-0630-4
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DOI: https://doi.org/10.1007/s11253-012-0630-4