Control and estimation of the boundary heat transfer function in Stefan problems

V. Barbu; K. Kunisch; W. Ring

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1996)

  • Volume: 30, Issue: 6, page 671-710
  • ISSN: 0764-583X

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Barbu, V., Kunisch, K., and Ring, W.. "Control and estimation of the boundary heat transfer function in Stefan problems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 30.6 (1996): 671-710. <http://eudml.org/doc/193819>.

@article{Barbu1996,
author = {Barbu, V., Kunisch, K., Ring, W.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {free moving boundary; feedback control; one phase Stefan problems; inverse problem; least squares; Hilbert space methods; convex analysis; convergence; suboptimal solutions; numerical experiments; regularization methods},
language = {eng},
number = {6},
pages = {671-710},
publisher = {Dunod},
title = {Control and estimation of the boundary heat transfer function in Stefan problems},
url = {http://eudml.org/doc/193819},
volume = {30},
year = {1996},
}

TY - JOUR
AU - Barbu, V.
AU - Kunisch, K.
AU - Ring, W.
TI - Control and estimation of the boundary heat transfer function in Stefan problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1996
PB - Dunod
VL - 30
IS - 6
SP - 671
EP - 710
LA - eng
KW - free moving boundary; feedback control; one phase Stefan problems; inverse problem; least squares; Hilbert space methods; convex analysis; convergence; suboptimal solutions; numerical experiments; regularization methods
UR - http://eudml.org/doc/193819
ER -

References

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  1. [B1] V. BARBU, 1993, Analysis and Control of Nonlinear Infinite Dimensional Systems. Academic Press, New York. Zbl0776.49005MR1195128
  2. [B2] V. BARBU, 1991, The approximate solvability ot the inverse one phase Stefan problem, Internat. Series Numer. Math., 99, pp. 33-43, Birkhauser Verlag, Basel. Zbl0733.65092MR1118851
  3. [BBC] J. V. BECK, B. BLACKWELL and C. CLAIR. 1985, Inverse Heat Conduction, Wiley-Interscience. Zbl0633.73120
  4. [BDZ] V. BARBU, G. DA PRATO, J. P. ZOLÉSIO, 1991, Feedback controllability of the free boundary of the one phase Stefan problem, Diff. Integral Equs., 4, pp. 225-239. Zbl0728.49013MR1081181
  5. [BK1] V. BARBU, K. KUNISCH, Identification of nonlinear elliptic equations, (to appear). Zbl0865.35139MR1365132
  6. [BK2] V. BARBU, K. KUNISCH, Identification of nonlinear parabolic equations (to appear). MR1424370
  7. [Br1] H. BRÉZIS, 1972, Problèmes unilatéraux, J. Math. Pures Appl., 51, pp. 1-64. Zbl0237.35001MR428137
  8. [Br2] H. BRÉZIS, 1983, Analyse fonctionnelle, Dunod, Paris. Zbl0511.46001MR697382
  9. [C] J. R. CANNON, 1984The One Dimensional Heat Equation, Addison-Weseley Publ. Comp., Menlo Park. Zbl0567.35001MR747979
  10. [DZ] G. DA PRATO, J. P. ZOLÉSIO, 1988, An optimal control problem for a parabolic equation in noncylindrical domains, Systems & Control Letters, 11, pp 73-77. Zbl0656.49001MR949893
  11. [GLS] GRIPENBERG, S. LONDEN, and STAFFANS, 1990, Volterra Integral and Functional Equations, Cambridge University Press. Zbl0695.45002MR1050319
  12. [HN] K. H. HOFFMANN, M. NIEZGODKA, 1990, Control of evolutionary free boundary problems, in Fret Boundary Problems Theory and Applications, pp. 439-450, K. H. Hoffmann and J. Sprekels, eds., Pitman Research Notes in Mathematics 186, Longman, London. MR1081737
  13. [HS] K. H. HOFFMANN, J. SPREKELS, 1982, Real time control of the free boundary in a two phase Stefan problem, Numerical Functional Anal. Optimiz, 5, pp. 47-76. Zbl0502.49005MR703116
  14. [KMP] K. KUNISCH, K. MURPHY, and G. PEICHL, Estimation of the conductivity in the one-phase Stefan problem : Basic results, to appear in Bolletino Unione Mat. Italiana. Zbl0848.35140MR1328513
  15. [La] P. K. LAMM, Future-sequential regularization methods for ill-posed Volterra equations, to appear in J. Math. Anal. and Appl. Zbl0851.65094MR1354556
  16. [Li] J. L. LIONS, 1969, Quelques Méthodes de Résolutions de Problèmes aux Limites Nonlinéaires, Dunod, Paris. Zbl0189.40603
  17. [PW] H. PROTER, H. WEINBERGER, 1983, The Maximum Principle, Springer-Verlag, Berlin. 

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