Alternative approaches to the two-scale convergence

Luděk Nechvátal

Applications of Mathematics (2004)

  • Volume: 49, Issue: 2, page 97-110
  • ISSN: 0862-7940

Abstract

top
Two-scale convergence is a special weak convergence used in homogenization theory. Besides the original definition by Nguetseng and Allaire two alternative definitions are introduced and compared. They enable us to weaken requirements on the admissibility of test functions ψ ( x , y ) . Properties and examples are added.

How to cite

top

Nechvátal, Luděk. "Alternative approaches to the two-scale convergence." Applications of Mathematics 49.2 (2004): 97-110. <http://eudml.org/doc/33177>.

@article{Nechvátal2004,
abstract = {Two-scale convergence is a special weak convergence used in homogenization theory. Besides the original definition by Nguetseng and Allaire two alternative definitions are introduced and compared. They enable us to weaken requirements on the admissibility of test functions $\psi (x,y)$. Properties and examples are added.},
author = {Nechvátal, Luděk},
journal = {Applications of Mathematics},
keywords = {two-scale convergence; weak convergence; homogenization; two-scale convergence; weak convergence; homogenization},
language = {eng},
number = {2},
pages = {97-110},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Alternative approaches to the two-scale convergence},
url = {http://eudml.org/doc/33177},
volume = {49},
year = {2004},
}

TY - JOUR
AU - Nechvátal, Luděk
TI - Alternative approaches to the two-scale convergence
JO - Applications of Mathematics
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 2
SP - 97
EP - 110
AB - Two-scale convergence is a special weak convergence used in homogenization theory. Besides the original definition by Nguetseng and Allaire two alternative definitions are introduced and compared. They enable us to weaken requirements on the admissibility of test functions $\psi (x,y)$. Properties and examples are added.
LA - eng
KW - two-scale convergence; weak convergence; homogenization; two-scale convergence; weak convergence; homogenization
UR - http://eudml.org/doc/33177
ER -

References

top
  1. 10.1137/0523084, SIAM J.  Math. Anal 23 (1992), 1482–1518. (1992) Zbl0770.35005MR1185639DOI10.1137/0523084
  2. Two-scale convergence on periodic surfaces and applications, In: Proc. International Conference on Mathematical Modelling of Flow through Porous Media, World Scientific Pub., Singapore, 1995, pp. 15–25. (1995) 
  3. Multiscale convergence and reiterated homogenization, Proc. Roy. Soc. Edinburgh 126 (1996), 297–342. (1996) MR1386865
  4. Two-scale convergence and homogenization on  BV ( Ω ) , Asymptot. Anal. 16 (1998), 65–84. (1998) MR1600123
  5. 10.1137/0521046, SIAM J.  Math. Anal. 21 (1990), 823–836. (1990) MR1052874DOI10.1137/0521046
  6. 10.1017/S0308210500021466, Proc. Roy. Soc. Edinburgh 129 (1999), 467–476. (1999) Zbl0946.46021MR1693641DOI10.1017/S0308210500021466
  7. 10.1137/S0036141000370260, SIAM J.  Math. Anal. 32 (2001), 1198–1226. (2001) MR1856245DOI10.1137/S0036141000370260
  8. Stochastic two-scale convergence in the mean and applications, J.  Reine Angew. Math. 456 (1994), 19–51. (1994) MR1301450
  9. A general compactness result and its application to the two-scale convergence of almost periodic functions, C. R.  Acad. Sci. Paris Sér.  I  Math. 323 (1996), 329–334. (1996) MR1408763
  10. Two-scale convergence for nonlinear Dirichlet problems in perforated domains, Proc. Roy. Soc. Edinburgh 130 (2000), 249–276. (2000) MR1750830
  11. 10.1016/S0764-4442(00)01794-8, C.  R.  Acad. Sci. Paris Sér.  I Math. 332 (2001), 223–228. (2001) MR1817366DOI10.1016/S0764-4442(00)01794-8
  12. 10.1016/S1631-073X(02)02429-9, C.  R.  Acad. Sci. Paris Sér.  I Math. 335 (2002), 99–104. (2002) MR1921004DOI10.1016/S1631-073X(02)02429-9
  13. Two-scale convergence of a model for flow in a partially fissured medium, Electron. J. Differential Equations 2 (1999), 1–20. (1999) MR1670679
  14. 10.1002/1521-4001(200009)80:9<579::AID-ZAMM579>3.0.CO;2-2, Z. Angew. Math. Mech. 80 (2000), 579–590. (2000) MR1778561DOI10.1002/1521-4001(200009)80:9<579::AID-ZAMM579>3.0.CO;2-2
  15. 10.1023/A:1023049608047, Appl. Math. 47 (1997), 321–343. (1997) Zbl0898.35008MR1467553DOI10.1023/A:1023049608047
  16. Homogénéisation d’un circuit électrique, C.  R.  Acad. Sci. Paris Sér. II  b 324 (1997), 537–542. (French) (1997) Zbl0887.35016
  17. Two-scale convergence, Int. J.  Pure Appl. Math. 2 (2002), 35–86. (2002) MR1912819
  18. 10.1137/0520043, SIAM J.  Math. Anal. 20 (1989), 608–623. (1989) Zbl0688.35007MR0990867DOI10.1137/0520043
  19. Admissible functions in two-scale convergence, Port. Math. 54 (1997), 147–164. (1997) Zbl0886.35018MR1467199
  20. Time-dependent Stokes flow through a randomly perforated porous medium, Asymptot. Anal. 23 (2000), 257–272. (2000) Zbl0973.76087MR1784454
  21. 10.1070/SM2000v191n07ABEH000491, Sb. Math. 191 (2000), 973–1014. (2000) MR1809928DOI10.1070/SM2000v191n07ABEH000491

Citations in EuDML Documents

top
  1. Jan Franců, Modification of unfolding approach to two-scale convergence
  2. Luděk Nechvátal, Homogenization with uncertain input parameters
  3. Anders Holmbom, Jeanette Silfver, Nils Svanstedt, Niklas Wellander, On two-scale convergence and related sequential compactness topics
  4. Jeanette Silfver, On general two-scale convergence and its application to the characterization of G -limits
  5. Jan Franců, Nils E M Svanstedt, Some remarks on two-scale convergence and periodic unfolding

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.