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The approximate solvability of the inverse one phase Stefan problem

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Numerical Methods for Free Boundary Problems

Abstract

Let Ω be a bounded and open subset of R N with a sufficiently smooth boundary Γ and let σ ∈ C2() be given function on D 1 ⊂ Ω such that D t = {x ∈ Ω; σ(x) < t} is increasing in t, σ(x) = 0 for xD 0, D T = D 1 (Fig.1 below).

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References

  1. V.Barbu, “Optimal Control of Variational Inequalities,” Pitman, London, 1984.

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  2. V.Barbu, The inverse one phase Stefan problem,Differential and Integral Equations 3, 2 (1990), 209–218.

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  3. K.H.Hoffman and N.Niezgodka, Control of parabolic systems involving free boundaries,in “Free Boundary Problems, Theory and Applications Vol.2,” Fasano and Primicerio eds. Pitman, 1983, pp. 431–462.

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  4. P.Jochum, The inverse Stefan problem as a problem of nonlinear approximation theory,J.Approximation Theory 30 (1980), 81–98.

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  5. J.CH.Saguez, “Contrôle optimal de systèmes à frontière libre,” Thèse d’Etat, l’Université de Technologie de Compiègne, 1980.

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© 1991 Springer Basel AG

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Barbu, V. (1991). The approximate solvability of the inverse one phase Stefan problem. In: Neittaanmäki, P. (eds) Numerical Methods for Free Boundary Problems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 99. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5715-4_2

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  • DOI: https://doi.org/10.1007/978-3-0348-5715-4_2

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5717-8

  • Online ISBN: 978-3-0348-5715-4

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