Abstract
In this paper we consider the application of the domain control theory in parabolic systems for the approximation of two-phase one-dimensional Stefan problem [1]. In this approach the role of the control function is carried out by the free-boundary (or interface). We use the shape penalty method [2,3] and investigate the corresponding approximation family of control bilinear systems and prove the theorem about uniform approximation. It is shown that classical solution of Stefan problem is a limit of the approximation solutions.
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References
Meirmanov A.M. The Stefan problem, Novosibirsk: Nauka, 1986 (in Russian).
Lions J.L. Quelques methodes de resolution des problemes aux limites non lineares, Dunod, Paris, 1969.
Ohezin S.P. On the approximation in domain control problem for parabolic system, Prikl. Ma. Mekh., v. 54, N 3, 1990, pp.361–365 (in Russian).
Ohezin S.P. On the mathematical model for Stefan problem. Dif. Uravneniia, v.27, N 6, 1991, pp. 1042–1048 (in Russian).
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© 1992 Springer Basel AG
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Ohezin, S.P. (1992). Optimal Shape Design for Parabolic System and Two-Phase Stefan Problem. In: Antontsev, S.N., Khludnev, A.M., Hoffmann, KH. (eds) Free Boundary Problems in Continuum Mechanics. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 106. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8627-7_27
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DOI: https://doi.org/10.1007/978-3-0348-8627-7_27
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9705-1
Online ISBN: 978-3-0348-8627-7
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