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 Electronic Journal of Probability > Vol. 14 (2009) > Paper 18 open journal systems 


Homogenization of semilinear PDEs with discontinuous averaged coefficients

Khaled Bahlali, Université de Toulon
A Elouaflin, Université de Cocody
Etienne Pardoux, Université de Provence


Abstract
We study the asymptotic behavior of solutions of semilinear PDEs. Neither period- icity 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 asso- ciated backward stochastic dierential equation (BSDE) in the Jakubowski S-topology to derive the averaged PDE. However, since the averaged coecients are discontinu- ous, the classical viscosity solution is not dened for the averaged PDE. We then use the notion of "Lp -viscosity solution" introduced in [7]. The existence of Lp -viscosity solution to the averaged PDE is proved here by using BSDEs techniques.


Full text: PDF

Pages: 477-499

Published on: February 22, 2009
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Electronic Journal of Probability. ISSN: 1083-6489