Abstract
The contribution is devoted to multi-dimensional two-phase problems of Stefan type involving some degenerations, and to related problems of optimal control. A problem with non-negative “specific heat” coefficient is considered. The existence of a weak solution to this problem is shown, uniqueness and stability results are presented. For a class of related typical optimal control problems results concerning existence of optimal controls are given. Approximations to these problems, based on regularization of the enthalpy, are introduced(the auxiliary nonlinear boundary value problems involve no more free boundary). Results on the convergence of optimal controls are presented.
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Niezgódka, M. (1982). Some Aspects of Approximation of Optimal Control Problems for Systems Governed by Parabolic Problems Involving Free Boundaries. In: Albrecht, J., Collatz, L., Hoffmann, KH. (eds) Numerical Treatment of Free Boundary Value Problems / Numerische Behandlung freier Randwertaufgaben. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 58. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6563-0_16
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DOI: https://doi.org/10.1007/978-3-0348-6563-0_16
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