A nonhomogenizable linear transport equation in ${ℝ}^{2}$
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 8 (2009) no. 1, p. 175-206
In this paper I investigate the homogenizability of linear transport equations with periodic data. Some results on homogenizability and on the form of the limit are known in literature. In particular, in [9], I proved the homogenizability in the two-dimensional case for nonvanishing functions, and, on the other hand I gave an example of a nonhomogenizable equation in the three-dimensional case. In this paper, I describe an example of a nonhomogenizable equation in two dimensions. As in [9], I study the problem using an equivalent formulation in terms of dynamical system properties of the associated ODEs.
Classification:  35B27,  37E45
@article{ASNSP_2009_5_8_1_175_0,
author = {Peirone, Roberto},
title = {A nonhomogenizable linear transport equation in $\mathbb{R}^2$},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 8},
number = {1},
year = {2009},
pages = {175-206},
zbl = {1184.35038},
mrnumber = {2512205},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2009_5_8_1_175_0}
}

Peirone, Roberto. A nonhomogenizable linear transport equation in $\mathbb{R}^2$. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 8 (2009) no. 1, pp. 175-206. http://www.numdam.org/item/ASNSP_2009_5_8_1_175_0/

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