Homogenization with uncertain input parameters

Luděk Nechvátal

Mathematica Bohemica (2010)

  • Volume: 135, Issue: 4, page 393-402
  • ISSN: 0862-7959

Abstract

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We homogenize a class of nonlinear differential equations set in highly heterogeneous media. Contrary to the usual approach, the coefficients in the equation characterizing the material properties are supposed to be uncertain functions from a given set of admissible data. The problem with uncertainties is treated by means of the worst scenario method, when we look for a solution which is critical in some sense.

How to cite

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Nechvátal, Luděk. "Homogenization with uncertain input parameters." Mathematica Bohemica 135.4 (2010): 393-402. <http://eudml.org/doc/196758>.

@article{Nechvátal2010,
abstract = {We homogenize a class of nonlinear differential equations set in highly heterogeneous media. Contrary to the usual approach, the coefficients in the equation characterizing the material properties are supposed to be uncertain functions from a given set of admissible data. The problem with uncertainties is treated by means of the worst scenario method, when we look for a solution which is critical in some sense.},
author = {Nechvátal, Luděk},
journal = {Mathematica Bohemica},
keywords = {homogenization; uncertain input data; worst scenario; homogenization; uncertain input data; worst scenario},
language = {eng},
number = {4},
pages = {393-402},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Homogenization with uncertain input parameters},
url = {http://eudml.org/doc/196758},
volume = {135},
year = {2010},
}

TY - JOUR
AU - Nechvátal, Luděk
TI - Homogenization with uncertain input parameters
JO - Mathematica Bohemica
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 135
IS - 4
SP - 393
EP - 402
AB - We homogenize a class of nonlinear differential equations set in highly heterogeneous media. Contrary to the usual approach, the coefficients in the equation characterizing the material properties are supposed to be uncertain functions from a given set of admissible data. The problem with uncertainties is treated by means of the worst scenario method, when we look for a solution which is critical in some sense.
LA - eng
KW - homogenization; uncertain input data; worst scenario; homogenization; uncertain input data; worst scenario
UR - http://eudml.org/doc/196758
ER -

References

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  7. Hlaváček, I., Chleboun, J., Babuška, I., Uncertain Input Data Problems and the Worst Scenario Method, Elsevier, Amsterdam (2004). (2004) Zbl1116.74003MR2285091
  8. Lukkassen, D., Meidell, A., Wall, P., 10.3934/dcds.2008.22.711, Discrete Contin. Dyn. Syst. 22 (2008), 711-727. (2008) Zbl1156.35314MR2429861DOI10.3934/dcds.2008.22.711
  9. Lukkassen, D., Nguetseng, G., Wall, P., Two-scale convergence, Int. J. Pure Appl. Math. 2 (2002), 35-86. (2002) Zbl1061.35015MR1912819
  10. Murat, F., Tartar, L., H-convergence, Topics in Mathematical Modelling of Composite Materials Birkhäuser, Boston (1997), 21-43. (1997) Zbl0920.35019MR1493039
  11. Nechvátal, L., 10.1023/B:APOM.0000027218.04167.9b, Appl. Math. 49 (2004), 97-110. (2004) Zbl1099.35012MR2043076DOI10.1023/B:APOM.0000027218.04167.9b
  12. Nechvátal, L., 10.1007/s10492-006-0015-9, Appl. Math. 51 (2006), 263-294. (2006) Zbl1164.35317MR2228666DOI10.1007/s10492-006-0015-9
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