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Homogenization of semilinear PDEs with discontinuous averaged coefficients

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1.	Title	Title of document	Homogenization of semilinear PDEs with discontinuous averaged coefficients
2.	Creator	Author's name, affiliation, country	Khaled Bahlali; Université de Toulon
2.	Creator	Author's name, affiliation, country	A Elouaflin; Université de Cocody
2.	Creator	Author's name, affiliation, country	Etienne Pardoux; Université de Provence
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Backward stochastic differential equations (BSDEs), $L^p$-viscosity solution for PDEs, homogenization, Jakubowski S-topology, limit in the Cesaro sense
3.	Subject	Subject classification	60H20, 60H30, 35K60
4.	Description	Abstract	We study the asymptotic behavior of solutions of semilinear PDEs. Neither periodicity nor ergodicity will be assumed. On the other hand, we assume that the coecients have averages in the Cesaro sense. In such a case, the averaged coecients could be discontinuous. We use a probabilistic approach based on weak convergence of the associated backward stochastic dierential equation (BSDE) in the Jakubowski $S$-topology to derive the averaged PDE. However, since the averaged coecients are discontinuous, the classical viscosity solution is not dened for the averaged PDE. We then use the notion of "$L_p$-viscosity solution" introduced in [7]. The existence of $L_p$-viscosity solution to the averaged PDE is proved here by using BSDEs techniques.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	PHC Tassili 07MDU705 and Marie Curie ITN, no. 213841-2 and AUF bourse post-doctorale 07-08, Réf.: PC-420/2460
7.	Date	(YYYY-MM-DD)	2009-02-22
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/627
10.	Identifier	Digital Object Identifier	10.1214/EJP.v14-627
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 14
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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