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 -

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