Homogenization of periodic semilinear hypoelliptic PDEs

Alassane Diédhiou[1]; Étienne Pardoux[2]

  • [1] Département de Mathématiques-Informatique, Faculté des Sciences et Technique, Université Cheikh Anta Diop, B.P. 5005 Dakar-Fann, Sénégal
  • [2] L.A.T.P, Université de Provence, 39 rue F. Joliot Curie, 13453 Marseille cedex 13, France

Annales de la faculté des sciences de Toulouse Mathématiques (2007)

  • Volume: 16, Issue: 2, page 253-283
  • ISSN: 0240-2963

Abstract

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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.

How to cite

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Diédhiou, Alassane, and Pardoux, Étienne. "Homogenization of periodic semilinear hypoelliptic PDEs." Annales de la faculté des sciences de Toulouse Mathématiques 16.2 (2007): 253-283. <http://eudml.org/doc/10048>.

@article{Diédhiou2007,
abstract = {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.},
affiliation = {Département de Mathématiques-Informatique, Faculté des Sciences et Technique, Université Cheikh Anta Diop, B.P. 5005 Dakar-Fann, Sénégal; L.A.T.P, Université de Provence, 39 rue F. Joliot Curie, 13453 Marseille cedex 13, France},
author = {Diédhiou, Alassane, Pardoux, Étienne},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {probabilistic method},
language = {eng},
number = {2},
pages = {253-283},
publisher = {Université Paul Sabatier, Toulouse},
title = {Homogenization of periodic semilinear hypoelliptic PDEs},
url = {http://eudml.org/doc/10048},
volume = {16},
year = {2007},
}

TY - JOUR
AU - Diédhiou, Alassane
AU - Pardoux, Étienne
TI - Homogenization of periodic semilinear hypoelliptic PDEs
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2007
PB - Université Paul Sabatier, Toulouse
VL - 16
IS - 2
SP - 253
EP - 283
AB - 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.
LA - eng
KW - probabilistic method
UR - http://eudml.org/doc/10048
ER -

References

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  13. Pardoux (É.).— Homogenization of Linear and Semilinear Second Order Parabolic PDEs with Periodic Coefficients: A Probabilistic Approch, Journal of Functional Analysis 167, p. 498-520, (1999). Zbl0935.35010MR1716206
  14. Pardoux (É.).— BSDEs, weak convergence and homogenization of semilinear PDEs, in “ Nonlinear Analysis, Differential Equations and Control” (F. H. Clarke and R. J. Stern, EDs.), p. 503-549, Kluwer Acad. Pub., (1999). Zbl0959.60049
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