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.
@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}, pages = {175--206}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 8}, number = {1}, year = {2009}, mrnumber = {2512205}, zbl = {1184.35038}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2009_5_8_1_175_0/} }
TY - JOUR AU - Peirone, Roberto TI - A nonhomogenizable linear transport equation in $\mathbb{R}^2$ JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2009 SP - 175 EP - 206 VL - 8 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2009_5_8_1_175_0/ LA - en ID - ASNSP_2009_5_8_1_175_0 ER -
%0 Journal Article %A Peirone, Roberto %T A nonhomogenizable linear transport equation in $\mathbb{R}^2$ %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2009 %P 175-206 %V 8 %N 1 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2009_5_8_1_175_0/ %G en %F 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, Serie 5, Volume 8 (2009) no. 1, pp. 175-206. http://archive.numdam.org/item/ASNSP_2009_5_8_1_175_0/
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