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Differentiable dependence upon the data in a one‐phase Stefan problem
Author(s) -
Jochum P.,
Brosowski B.
Publication year - 1980
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670020108
Subject(s) - mathematics , stefan problem , differentiable function , fréchet derivative , boundary (topology) , operator (biology) , free boundary problem , derivative (finance) , boundary value problem , mathematical analysis , phase (matter) , banach space , biochemistry , chemistry , organic chemistry , repressor , transcription factor , financial economics , economics , gene
It is well known that the free boundary of the one‐phase Stefan problem (1.1–5) depends continuously on the boundary data [1]. In this paper we prove that, in addition, the solution operator S which, to each g . assigns the corresponding free boundary, is continuously Frechet differentiable and we give the defining formulas of the Frechet derivative.