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Optimal control for parabolic systems with free boundaries — Existence of optimal controls, approximation results

  • Marek Niezgódka
  • Irena Pawłow
Optimal Control: Partial Differential Equations
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 22)

Abstract

The paper is concerned with optimal control problems for systems governed by multidimensional two-phase parabolic free boundary value problems of Stefan type. In the case of nonlinear process equations and nonlinear boundary conditions existence of optimal controls enclosed in these conditions and convergence of approximating optimal control problems including smoothed coefficients are shown.

Keywords

Weak Solution Optimal Control Problem Free Boundary Weak Formulation Parabolic System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    B.M. Budak and Yu.L. Gaponenko, On the solution of Stefan problem involving quasilinear parabolic equation and quasilinear boundary conditions, Trudy Vyčisl. Centra MGU, 1971. (in Russian)Google Scholar
  2. [2]
    B.M. Budak, E.N. Solov'eva and A.B. Uspenskii, Finite difference method with coefficients smoothing for solving Stefan problems, Žurnal Vyčisl. Matematiki i Matem. Fiziki, 5 (1965). (in Russian)Google Scholar
  3. [3]
    A. Friedman, The Stefan problem in several space variables, Trans. Amer. Math. Society, 133 (1968).Google Scholar
  4. [4]
    S. Kamenomotskaya, On the Stefan problem, Mat. Sbornik, 53 (95) (1961). (in Russian)Google Scholar
  5. [5]
    O.A. Ladyženskaya, V.S. Solonnikov and N.N. Ural'ceva, Linear and quasilinear equations of parabolic type, Nauka, Moskva 1967. (in Russian)Google Scholar
  6. [6]
    J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Vol. 1 et 2, Dunod, Paris 1968.Google Scholar
  7. [7]
    M. Niezgódka and I. Pawłow, Optimal control of a Stefan type process, (to appear).Google Scholar
  8. [8]
    M. Niezgódka and I. Pawłow, A generalized Stefan problem in several space variables, (to appear).Google Scholar
  9. [9]
    J.R. Ockendon and W.R. Hodgkins, eds., Moving boundary problems in heat flow and diffusion, Clarendon Press, Oxford 1975.Google Scholar
  10. [10]
    O.A. Oleinik, A method of solution of the general Stefan problem, DAN SSSR, 135 (1960). (in Russian)Google Scholar
  11. [11]
    C. Saguez, Contrôle optimal de systèmes gouvernés par des inéquations variationnelles; applications à des problemes de frontière libre, IRIA, Rapport de Recherche 1976.Google Scholar
  12. [12]
    D.G. Wilson, A.D. Solomon and P.T. Boggs, eds,, Moving boundary problems, Academic Press, New York 1978.Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Marek Niezgódka
    • 1
  • Irena Pawłow
    • 1
  1. 1.Systems Research InstitutePolish Academy of SciencesWarszawaPoland

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