The approximate solvability of the inverse one phase Stefan problem.(English)Zbl 0733.65092

Numerical methods for free boundary problems, Proc. Conf., Jyväskylä/Finl. 1990, ISNM 99, 33-43 (1991).
[For the entire collection see Zbl 0722.00035.]
The author studies the inverse one phase Stefan problem and proves that under some conditions this problem is approximately solvable in a certain sense. The key idea of the proof is to approximate the inverse Stefan problem by an appropriate optimal control problem, which represents a parabolic boundary problem and can be then investigated by using the standard Sobolev space technique.
Reviewer: O.Titow (Berlin)

MSC:

 65Z05 Applications to the sciences 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 35K05 Heat equation 35R30 Inverse problems for PDEs 35R35 Free boundary problems for PDEs 80A22 Stefan problems, phase changes, etc. 80A23 Inverse problems in thermodynamics and heat transfer

Zbl 0722.00035