When does Agglutination Arise in the Homogeneization of Ordinary Differential Equations?

Bosa, Elena ; Piccinini, Livio C.

Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 2, pp. 361-374

Résumé

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.