Reliable solution of parabolic obstacle problems with respect to uncertain data

Ján Lovíšek

Applications of Mathematics (2003)

  • Volume: 48, Issue: 5, page 321-351
  • ISSN: 0862-7940

Abstract

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A class of parabolic initial-boundary value problems is considered, where admissible coefficients are given in certain intervals. We are looking for maximal values of the solution with respect to the set of admissible coefficients. We give the abstract general scheme, proposing how to solve such problems with uncertain data. We formulate a general maximization problem and prove its solvability, provided all fundamental assumptions are fulfilled. We apply the theory to certain Fourier obstacle type maximization problem.

How to cite

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Lovíšek, Ján. "Reliable solution of parabolic obstacle problems with respect to uncertain data." Applications of Mathematics 48.5 (2003): 321-351. <http://eudml.org/doc/33151>.

@article{Lovíšek2003,
abstract = {A class of parabolic initial-boundary value problems is considered, where admissible coefficients are given in certain intervals. We are looking for maximal values of the solution with respect to the set of admissible coefficients. We give the abstract general scheme, proposing how to solve such problems with uncertain data. We formulate a general maximization problem and prove its solvability, provided all fundamental assumptions are fulfilled. We apply the theory to certain Fourier obstacle type maximization problem.},
author = {Lovíšek, Ján},
journal = {Applications of Mathematics},
keywords = {uncertain data; optimal design approach; parabolic obstacle problems; penalization method; Fourier problem; uncertain data; optimal design approach; parabolic obstacle problems; penalization method; Fourier problem},
language = {eng},
number = {5},
pages = {321-351},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Reliable solution of parabolic obstacle problems with respect to uncertain data},
url = {http://eudml.org/doc/33151},
volume = {48},
year = {2003},
}

TY - JOUR
AU - Lovíšek, Ján
TI - Reliable solution of parabolic obstacle problems with respect to uncertain data
JO - Applications of Mathematics
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 5
SP - 321
EP - 351
AB - A class of parabolic initial-boundary value problems is considered, where admissible coefficients are given in certain intervals. We are looking for maximal values of the solution with respect to the set of admissible coefficients. We give the abstract general scheme, proposing how to solve such problems with uncertain data. We formulate a general maximization problem and prove its solvability, provided all fundamental assumptions are fulfilled. We apply the theory to certain Fourier obstacle type maximization problem.
LA - eng
KW - uncertain data; optimal design approach; parabolic obstacle problems; penalization method; Fourier problem; uncertain data; optimal design approach; parabolic obstacle problems; penalization method; Fourier problem
UR - http://eudml.org/doc/33151
ER -

References

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  1. Un théorème de compacité, C. R. Acad. Sci. Paris 256 (1963), 5042–5044. (1963) Zbl0195.13002MR0152860
  2. Optimal Control of Variational Inequalities, Pitman, Boston, 1984. (1984) Zbl0574.49005MR0742624
  3. 10.1002/mana.19861250109, Math. Nachr. 125 (1968), 135–151. (1968) MR0847355DOI10.1002/mana.19861250109
  4. Problèmes unilatéraux, J. Math. Pures Appl. 51 (1972), 1–168. (1972) 
  5. Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North Holland, Amsterdam, 1973. (1973) MR0348562
  6. Analyse fonctionelle, Masson, Paris, 1982. (1982) 
  7. Nichtlineare Operatorgleichungen und Operator-Differentialgleichungen, Akademie, Berlin, 1974. (1974) MR0636412
  8. 10.1016/S0362-546X(96)00236-2, Nonlinear Anal. 30 (1997), 3879–3980. (1997) MR1602891DOI10.1016/S0362-546X(96)00236-2
  9. 10.1002/(SICI)1521-4001(199905)79:5<291::AID-ZAMM291>3.0.CO;2-N, Z.  Angew. Math. Mech. 79 (1999), 291–301. (1999) MR1695286DOI10.1002/(SICI)1521-4001(199905)79:5<291::AID-ZAMM291>3.0.CO;2-N
  10. Contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles, Dunod, Paris, 1968. (1968) MR0244606
  11. Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969. (1969) Zbl0189.40603MR0259693
  12. Optimization in Elliptic Problems with Applications to Mechanics of Deformable Bodies and Fluid Mechanics, Birkhäuser-Verlag, Berlin, 2000. (2000) Zbl0947.49001MR1774123
  13. 10.1137/0322028, SIAM J.  Control Optim. 22 (1984), 466–478. (1984) MR0739836DOI10.1137/0322028
  14. 10.1016/0001-8708(69)90009-7, Adv. Math. 3 (1969), 510–585. (1969) MR0298508DOI10.1016/0001-8708(69)90009-7
  15. Les méthodes directes en théorie des équations elliptiques, Masson, Paris, 1967. (1967) MR0227584
  16. Optimal Control of Nonlinear Parabolic Systems. Theory, Algorithms and Applications. Pure and Applied Mathematics, Marcel Dekker inc., New York, 1994. (1994) MR1275836
  17. 10.1137/0320054, SIAM J. Control Optim. 20 (1982), 747–762. (1982) MR0675567DOI10.1137/0320054
  18. Introduction to Shape Optimization. Shape Sensitivity Analysis, Springer-Verlag, New York, 1992. (1992) MR1215733
  19. Contrôle optimal de systèmes gouvernés par des inéquations variationnelles, Rapport de Recherche 22, INRIA, Paris, 1974. (1974) 
  20. A Variational Inequality Approach to Free Boundary Problems with Applications in Mould Filling, Birkhäuser-Verlag, Basel, 2002. (2002) Zbl1011.35001MR1891393
  21. Elliptic Differential Equations and Obstacle Problems, Plenum Press, New York, 1987. (1987) Zbl0655.35002MR1094820
  22. Nonlinear Functional Analysis and its Applications II/A, Linear Monotone Operators, Springer-Verlag, New York, 1990. (1990) Zbl0684.47028MR1033497

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