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.
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