When does Agglutination Arise in the Homogeneization of Ordinary Differential Equations?
Elena Bosa; Livio C. Piccinini
Bollettino dell'Unione Matematica Italiana (2008)
- Volume: 1, Issue: 2, page 361-374
- ISSN: 0392-4041
Access Full Article
top
Abstract
topHow to cite
topBosa, Elena, and Piccinini, Livio C.. "When does Agglutination Arise in the Homogeneization of Ordinary Differential Equations?." Bollettino dell'Unione Matematica Italiana 1.2 (2008): 361-374. <http://eudml.org/doc/290481>.
@article{Bosa2008,
abstract = {When dealing with Differential Equations whose coefficients are periodical, it is of interest to consider the limit when the period becomes shorter and shorter. This process is called homogeneization and leads to an equation with constant coefficients. The constants are some mean of the original coefficients, usually non trivial. We say that the mean is regular if it is increased whenever coefficients are increased on a non-zero set; on the contrary we say that agglutination arises if there are intervals of constancy. It is well known that a chessboard structure leads to agglutination. The authors give some sufficient conditions to prevent agglutination and show that some more general forms of mosaic can not save regularity.},
author = {Bosa, Elena, Piccinini, Livio C.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {361-374},
publisher = {Unione Matematica Italiana},
title = {When does Agglutination Arise in the Homogeneization of Ordinary Differential Equations?},
url = {http://eudml.org/doc/290481},
volume = {1},
year = {2008},
}
TY - JOUR
AU - Bosa, Elena
AU - Piccinini, Livio C.
TI - When does Agglutination Arise in the Homogeneization of Ordinary Differential Equations?
JO - Bollettino dell'Unione Matematica Italiana
DA - 2008/6//
PB - Unione Matematica Italiana
VL - 1
IS - 2
SP - 361
EP - 374
AB - When dealing with Differential Equations whose coefficients are periodical, it is of interest to consider the limit when the period becomes shorter and shorter. This process is called homogeneization and leads to an equation with constant coefficients. The constants are some mean of the original coefficients, usually non trivial. We say that the mean is regular if it is increased whenever coefficients are increased on a non-zero set; on the contrary we say that agglutination arises if there are intervals of constancy. It is well known that a chessboard structure leads to agglutination. The authors give some sufficient conditions to prevent agglutination and show that some more general forms of mosaic can not save regularity.
LA - eng
UR - http://eudml.org/doc/290481
ER -
References
top- BOETTCHER, S. - PACZUSKI, M., Exact results for Spatiotemporal Correlations in a Self-organized Critical Model of Punctuated Equilibrium. Phys. Rev. Lett., 76 (1996), 348-351.
- MORTOLA, S. - PEIRONE, R., Omogeneizzazione di una equazione differenziale ordinaria avente struttura a scacchiera. Rend. Mat. Acc. Lincei, 2 (1991), no. 1, 5-10.
- PEIRONE, R., Rotation number of ODE's with a chessboard structure, Non linearity, 6, fasc 4 (1993), 617-652. Zbl0786.58023MR1231776
- PICCININI, L. C., Homogeneization for ordinary differential equations. Rend. Circ. Mat. Palermo, 27 (1978), 95-112. Zbl0416.34019MR542236DOI10.1007/BF02843869
- PICCININI, L. C., Linearity and non-linearity in the theory of G-convergence in Recent Advances in Differential Equations. Edit. R. ContiAcademic PressNew York (1981), 337-372. MR643145
- PICCININI, L. C. - STAMPACCHIA, G. - VIDOSSSICH, G., Ordinary differential Equations in . Springer VerlagNew York (1984), 187-202. Translation into English of Equazioni differenziali in , Liguori Ed.Napoli (1978). MR740539DOI10.1007/978-1-4612-5188-0
NotesEmbed ?
topYou 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.