We establish homogenization results for both linear and semilinear partial differential equations of parabolic type, when the linear second order PDE operator satisfies a hypoellipticity asumption, rather than the usual ellipticity condition. Our method of proof is essentially probabilistic.
Nous établissons des résultats d’homogénéisation d’équations aux dérivées partielles paraboliques linéaires et semi–linéaires, sous une hypothèse d’hypoellipticité de l’opérateur aux dérivées partielles du second ordre, au lieu de l’hypothèse usuelle d’ellipticité. Notre méthode de démonstration est essentiellement probabiliste.
@article{AFST_2007_6_16_2_253_0,
author = {Alassane Di\'edhiou and \'Etienne Pardoux},
title = {Homogenization of periodic semilinear hypoelliptic {PDEs}},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {253--283},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 16},
number = {2},
year = {2007},
doi = {10.5802/afst.1148},
mrnumber = {2331541},
zbl = {1131.35304},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1148/}
}
TY - JOUR AU - Alassane Diédhiou AU - Étienne Pardoux TI - Homogenization of periodic semilinear hypoelliptic PDEs JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2007 SP - 253 EP - 283 VL - 16 IS - 2 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1148/ DO - 10.5802/afst.1148 LA - en ID - AFST_2007_6_16_2_253_0 ER -
%0 Journal Article %A Alassane Diédhiou %A Étienne Pardoux %T Homogenization of periodic semilinear hypoelliptic PDEs %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2007 %P 253-283 %V 16 %N 2 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1148/ %R 10.5802/afst.1148 %G en %F AFST_2007_6_16_2_253_0
Alassane Diédhiou; Étienne Pardoux. Homogenization of periodic semilinear hypoelliptic PDEs. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 16 (2007) no. 2, pp. 253-283. doi : 10.5802/afst.1148. https://afst.centre-mersenne.org/articles/10.5802/afst.1148/
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